diff --git "a/1dE4T4oBgHgl3EQfaAyc/content/tmp_files/load_file.txt" "b/1dE4T4oBgHgl3EQfaAyc/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/1dE4T4oBgHgl3EQfaAyc/content/tmp_files/load_file.txt" @@ -0,0 +1,3432 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf,len=3431 +page_content='PREPRINT Electroweak Phase Transition in a Right-Handed Neutrino Superfield Extended NMSSM Pankaj Borah,a Pradipta Ghosh,a Sourov Royb and Abhijit Kumar Sahab aDepartment of Physics, Indian Institute of Technology Delhi, Hauz Khas 110 016, India bSchool of Physical Sciences, Indian Association for the Cultivation of Science, 2A & 2B Raja S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mullick Road, Kolkata 700 032, India E-mail: Pankaj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='Borah@physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='iitd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='in, tphyspg@physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='iitd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='in, tpsr@iacs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='in, psaks2484@iacs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='in Abstract: Supersymmetric models with singlet extensions can accommodate single- or multi-step first-order phase transitions (FOPT) along the various constituent field direc- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Such a framework can also produce Gravitational Waves, detectable at the upcom- ing space-based interferometers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', U-DECIGO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We explore the dynamics of electroweak phase transition and the production of Gravitational Waves in an extended set-up of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) with a Standard Model sin- glet right-handed neutrino superfield.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We examine the role of the new parameters compared to NMSSM on the phase transition dynamics and observe that the occurrence of a FOPT, an essential requirement for Electroweak Baryogenesis, typically favours a right-handed sneutrino state below 125 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Our investigation shows how the analysis can offer com- plementary probes for physics beyond the Standard Model besides the collider searches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='05061v1 [hep-ph] 12 Jan 2023 Contents 1 Introduction 2 2 The Model 5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 A convenient basis choice 8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 Higher order contributions 10 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Contributions from non-zero temperature 12 3 Choice of parameters 13 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 Experimental Constraints 15 4 The EWPT and its Properties 17 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 PT in the NMSSM + one RHN model 19 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 Numerical Results 20 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 GW spectrum from SFOPT in the NMSSM + one RHN model 28 5 Summary and Conclusion 36 A Field dependent mass matrices 38 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 CP-even neutral scalars squared mass matrix 40 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 CP-odd neutral scalars squared mass matrix 41 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Uncoloured charged scalars squared mass matrix 43 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 Neutralino mass matrix 45 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 Chargino mass matrix 45 B Neutral scalar mass matrices after the EWSB 46 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 CP-even mass squared elements 46 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 CP-odd mass squared elements 47 C Counter terms 47 D Daisy coefficients 48 E Minimization conditions 49 – 1 – 1 Introduction Baryon asymmetry of the Universe is a precisely measured quantity by Planck experiment [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Different kinds of proposals pertaining to baryon asymmetry production mechanism in the early Universe are prevalent in literature (for a brief summary see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In recent times, baryon asymmetry production during the Electroweak Phase Transition (EWPT), known as the Electroweak Baryogenesis (EWBG) [3] has gained particular attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The EWBG occurs around the TeV scale and has the potential to be probed in collider ex- periments [4–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Irrespective of different baryon asymmetry generation mechanisms, the Sakharov conditions [7], namely, (i) baryon number violation, (ii) charge (C) and charge- parity (CP) violation and (iii) deviation from thermal equilibrium must be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is well known that the Standard Model (SM) of particle physics fails to provide a sufficient departure from thermal equilibrium [8, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moreover, C and CP violations in the SM are not adequate enough to yield the observed baryon asymmetry of the Universe [8, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In principle, a strong first-order EWPT (SFOEWPT) in the early Universe can pave the way for the EWBG by allowing sufficient out-of-equilibrium processes [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The SM of par- ticle physics with the observed Higgs mass ∼ 125 GeV [11, 12], shows a smooth cross-over pattern along the Higgs field direction without any PT [13–15] and thus, fails to accom- modate the EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This issue can be circumvented by introducing new scalar degrees of freedom having sizeable coupling with the SM Higgs boson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In general, the strength of the EW phase transition is determined by both the high and low-temperature behaviour of the scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Computation of critical temperature reveals displacement of the global minimum for a scalar potential when expressed as a function of the temperature (T) of the Universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, a correct description of the EWPT requires the study of bubble nucleation dynamics since PT proceeds via the nucleation of bubbles [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The dynamics of bubble nucleation, during the first-order EWPT, can yield stochastic Gravitational Waves (GWs) in the early Universe [17–22] that may appear detectable at different GW experi- ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, the search for GWs for probing different kinds of beyond the SM (BSM) frameworks has long been practised (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [23–26] for some of the recent works).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Supersymmetric models, having a rich scalar sector compared to the SM, carry the necessary ingredients for exhibiting an SFOEWPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The PT properties in the Minimal Supersymmetric Standard Model (MSSM) (see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [27] for a review) are exercised in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [28–37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is shown in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [37] that a strong EWPT with a 125 GeV Higgs boson favours a hierarchical stop sector in the MSSM, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', one of two stops appears to be much heavier than the EW scale while the lighter one remains around O(100 GeV) [36, 37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The presence of such a light stop enhances the Higgs production rate through gluon-gluon fusion [37, 38] and confronts constraints from LHC data [11, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This tension, nevertheless, can be alleviated by considering a light neutralino with a mass lower than about 60 GeV [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, once again it is challenged by the LHC data of Higgs invisible decay width [39–42] and neutralino searches from the stop decay [43–45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, the MSSM also suffers from a new kind of naturalness problem known as the µ-problem [46] and, just like the SM, is incapable of accommodating non-zero neutrino masses and mixing [47, 48] in its original – 2 – form1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The Next-to-Minimal Supersymmetric Standard Model (NMSSM) [54] provides a dy- namical solution to the µ-problem, a challenge that has plagued the MSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the NMSSM, the scalar sector of the MSSM is further enriched by the presence of a gauge singlet scalar S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Studies related to EWPT in the NMSSM can be found in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [55–60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It has been observed [55–60] that in the NMSSM soft supersymmetry (SUSY) breaking term involving S and Higgs doublets assists to form the potential barrier even at T = 0 in contrast to the MSSM where T ̸= 0 effects are essential for barrier formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, the PT dynamics is more involved in the NMSSM where one needs to consider a three-dimensional field space spanned by three2 CP-even scalar fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The EWPT could occur either in single-step or multi-step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the NMSSM, both single-step and multi-step phase transitions are possible as discussed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [59, 60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These studies [59, 60] rely on an effective field theory set-up after integrating out heavy stops which yield potentially large contributions to the one-loop effective potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Such an effective-theory-based approach reduces the number of degrees of freedom participating in the EWPT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [59, 60] also showed that the NMSSM can accommodate EWBG in some region corners of the NMSSM parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Shifting our attention to non-zero neutrino masses and mixing [47, 48, 53], another experimentally established BSM signature, both MSSM and NMSSM, are futile just like the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Extensions of these models with additional ingredients, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', right-handed (RH) neutrinos, however, offer a simple elegant way to accommodate massive neutrinos using the popular type-I see-saw mechanism [62–65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Supersymmetric type-I seesaw mechanism, where the MSSM superfield content is extended with RH-neutrino superfield(s) is well stud- ied, see for example, Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [66–68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Incorporating RH-neutrino superfield(s) in the NMSSM provides a minimal model [69] where, apart from accommodating none-zero neutrino masses and mixing, one also gets a solution for the µ-problem3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In such a framework, non-zero neutrino masses appear through three sources: (i) type-I seesaw mechanism involving RH- neutrino(s), generally known as the “canonical seesaw”, (ii) type-I and type-III seesaw involving gauginos, popularly known as the “gaugino seesaw” and, (iii) seesaw involving higgsinos, better known as “higgsino seesaw” [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The last two pieces arise when left- handed (LH) and RH sneutrinos acquire vacuum expectation values (VEVs), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', R-parity gets spontaneously broken [73, 74] and e���ective bilinear R-parity-violating [49] terms are generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For this study, for simplicity, we considered the NMSSM framework extended with one RH-neutrino superfield.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One, however, needs at least two RH-neutrino superfields to accommodate the neutrino data, leaving the lightest one massless [75, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The chosen simple framework, nevertheless, offers a nice platform to investigate the PT dynamics and subsequently the predictions for GW emission, besides providing the correct scale for the 1MSSM extended with new superfields or new symmetries or R-parity violation [49] (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [50–52] for further reading) can accommodate neutrino data [47, 48, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R-parity is defined as RP = (−1)3B+L+2s where L(B) denotes the lepton (baryon) number and s represents the spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2The PT dynamics in guided by a two-dimensional field space in the MSSM [35, 61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 3An alternative minimal framework, known as µνSSM [70–72], also solves the µ-problem and satisfies the neutrino oscillation data simultaneously, even at the tree-level [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 3 – neutrino mass and the atmospheric mass-square difference [47, 48, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We plan to inves- tigate the possible correlations between the neutrino sector and the PT dynamics in the context of NMSSM with more than one family of RH-neutrino superfields in a forthcoming publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Restoring the discussion of PT dynamics, the electrically neutral uncoloured scalar sector of the NMSSM extended with one RH-neutrino superfield set-up possesses fourteen degrees of freedom, including the neutral Goldstone mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, as we will see later in section 2, the effective degrees of freedom appear to be eight owing to weak couplings of the LH-sneutrino states with the remaining states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Out of these eight, only four are CP-even in nature and actively participate in the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hence, the concerned field space is four-dimensional for the chosen framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This enhanced field space compared to the MSSM (two-dimensional due to two Higgses) and the NMSSM (three-dimensional owing to two Higgs doublets and one singlet), facilitates the study of EWPT, via single steps and multi-steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the numerical frontier, we adopt a benchmark-based analysis and finally select a few benchmark points (BPs) that appear promising from the viewpoint of EWBG and also exhibit distinct (single-step or two-steps) PT properties in the early Universe along the various constituent field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the later part, we exploit some of the BPs in order to further investigate the role of new parameters that appear in the setup due to the presence of RH-neutrino superfield in the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We also consider various relevant experimental constraints, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', collider, charged-lepton flavour violation, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', while choosing our BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, null experimental evidence of sparticles to date has put stringent lower bounds on the concerned states, especially the coloured ones [77–80].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, for the analysis of EWPT, we integrate such heavy states out and work in the context of a simplified effective model rather than considering the full NMSSM + one RH-neutrino framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have adopted both the critical and nucleation temperature analyses to describe the PT properties in our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This is crucial since earlier studies, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [60], have reported that the analysis of PT, solely based on critical temperature calculation does not provide a complete picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, the critical temperature analysis does not confirm whether a PT has indeed taken place or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A first-order phase transition (FOPT) proceeds via bubble nucleation and hence computation of nucleation probability and subsequently, nucleation temperature are vital to correctly describe the pattern of a FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, we discuss the detection prospects of all our BPs in the forthcoming GW interferometers and find that the future space-based experiments: namely, U-DECIGO and U-DECIGO-corr [81, 82], have the required sensitivities to test a few of our BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This possibility gives a complementary detection scope for the NMSSM + one RH-neutrino set-up beyond the conventional experimental searches, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', collider, neutrino, flavour, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The paper is organised as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In section 2 we discuss the model setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Next in section 3, we talk about the relevant model parameters that are important for studying the PT properties and the possible experimental constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Subsequently in section 4, we present the dynamics of EWPT in detail along with our numerical findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This section also addresses the production of the GW and the testability of our framework in upcoming space-based interferometers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', U-DECIGO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, we summarize our analysis and – 4 – conclude in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Some useful formulae and relations are relegated to the appendices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2 The Model The superpotential for the chosen framework is given by W = W ′ MSSM + λ �S �Hu · �Hd + κ 3 �S3 + Y i N � N �Li · �Hu + λN 2 �S � N � N, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where i = 1, 2, 3 denotes the generation indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) is nothing but the Z3 symmet- ric NMSSM superpotential, extended with one Right-Handed Neutrino (RHN) superfield ( ˆN), keeping the initial Z3 symmetry unbroken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here W ′ MSSM denotes the MSSM super- potential (see reviews [27, 83–85]) without the bilinear µ-term, ˆHu = ( ˆH+ u , ˆH0 u)T , ˆHd = ( ˆH0 d, ˆH− d )T , ˆLi = (ˆνi, ˆli)T are the SU(2)L doublet up-type Higgs, down-type Higgs, and lepton superfields, respectively and the “·” notation is used to express SU(2) product, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ˆLi · ˆHu = ˆνi ˆH0 u − ˆli ˆH+ u .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The superpotential in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) cannot be made invariant under a global U(1) symmetry, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', U(1) of the Lepton number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This in turn ensures the disap- pearance of a Nambu-Goldstone boson which results from the spontaneous breaking of a global symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The ˆN is considered to be odd under RP while the ˆS transforms as even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' RP is violated spontaneously in this model when, along with the other neutral scalars, the RH-sneutrino ( � N) also acquires a non-zero VEV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These VEVs yield the effective µ-term (µ = λ⟨S⟩), the effective bilinear RP -violating couplings (ϵi = Y i N⟨ � N⟩), and the Majorana mass term for the RHN (λN⟨S⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One should note the presence of four extra couplings (three neutrino Yukawa couplings Y 1,2,3 N and another trilinear coupling λN) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), apart from the known Z3 invariant NMSSM couplings, λ and κ (see for example Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [54, 86]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We would like to re-emphasize here that with only one ˆN, of course, one cannot reproduce the observed neutrino mass squared differences and mixing [47, 48, 53], even after including loop corrections [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, even this simple choice can predict the absolute mass scale and atmospheric mass squared difference for the active neutrinos, besides giving interesting information about the EWPT and GW, the primary goals of this article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We plan to explore the possible correlations between neutrino observable with the EWPT and GW sectors in the context of a two or three ˆN scenario [69] in future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Following Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), in a similar way, we can write down Lsoft, the piece of Lagrangian density that contains soft-SUSY breaking terms: −Lsoft = −L′soft + m2 S S∗S + M2 N � N∗ � N + � λAλS Hu · Hd + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' � + �κAκ 3 S3 + (ANYN)i �Li · Hu � N + AλN λN 2 S � N � N + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) where L′ soft contains the MSSM soft-supersymmetry breaking terms, excluding the Bµ term [27, 83–85, 87, 88].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The remaining terms are typical to that of the Z3 symmetric NMSSM, except the terms involving � N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Soft terms, as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2), are written in the framework of supergravity mediated SUSY breaking [89].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' All the trilinear A-terms and the soft squared masses are assumed to lie in the TeV regime and consequently, all VEVs – 5 – are expected to appear also in the same regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In other words, the scale of RHN mass, which is determined solely by the scale of soft-SUSY breaking terms will also lie in the TeV regime assuming λN ∼ O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This assures neutrino mass generation via the TeV scale seesaw mechanism which is also testable at colliders [90–95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, the TeV scale seesaw immediately suggests Y i N ∼ O (10−6 − 10−7) and left-handed sneutrino VEVs, ⟨�νi⟩ ∼ O (10−4 − 10−5) GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These values of Y i N, ⟨�νi⟩ indicate (i) tiny RP violation (∼ O (10−3 − 10−4) GeV, typical for the bilinear RP violation [96]) and, (ii) weak mixing of the left-handed leptons and sleptons (neutral and charged) with the concerned sectors, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', charged and neutral gauginos, higgsinos, Higgses, right-handed neutrino and sneutrino, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can use the advantage of such weak mixing to perform a simplified analysis without the loss of generality, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', using a set of four fields (Hu, Hd, S, ˜N) instead of seven (Hu, Hd, S, � N, �Li) while investigating the PT phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The tree-level neutral scalar potential is the sum of F-term (VF ), D-term (VD) and the soft-SUSY breaking terms and is given by Vtree = VF + VD + Vsoft, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) where Vsoft ≡ −Lsoft is given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' VF , following the usual prescription from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), is written as VF = ��� − λH0 uH0 d + κS2 + λN 2 � N2��� 2 + |Y i N|2 |H0 u|2| � N|2 + |λ|2|S|2|H0 u|2 + ��� 3 � i=1 Y i N �νiH0 u + λNS � N ��� 2 + ��� 3 � i=1 Y i N �νi � N − λSH0 d ��� 2 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) and VD, again using the standard procedure is read as VD = g2 1 + g2 2 8 � |H0 d|2 + 3 � i=1 |�νi|2 − |H0 u|2 �2 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) with g1, g2 as the U(1)Y , SU(2)L gauge couplings, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The neutral CP-even scalar components4, after the EW-symmetry breaking (EWSB), develop the following zero-temperature VEVs: ⟨H0 u⟩ = vu, ⟨H0 d⟩ = vd, ⟨S⟩ = vS, ⟨�νi⟩ = vi, ⟨ � N⟩ = vN, i = 1, 2, 3 or e, µ, τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) The first three VEVs are typical to the NMSSM while the last two VEVs appear for the chosen framework as a consequence of the spontaneous RP violation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can use these VEVs to trade off the concerned soft squared masses as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The VEVs vS, vN, being governed by the TeV scale soft-terms, also lie in the same regime whereas vi appears to be much smaller ∼ O(100 MeV) for vN, vS ∼ O(1 TeV) [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Generation of the neutrino mass via a TeV scale seesaw mechanism, as already advocated, however, offers 4Here we adhere to CP-conservation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, we do not consider the possibility of charge and colour- breaking minima for this study (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [97] in the context of the NMSSM) and hence, assign vanishing VEVs to charged and coloured scalars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 6 – a more stringent constraint on vi (∼ O (10−4 − 10−5) GeV), similar to models studied in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [73, 98–101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can write down minimization conditions for vN, vi, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3), as: ∂Vtree ∂ � N ��� VEVs as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) = λNvN � λvuvd + κv2 S + λN 2 v2 N � + |Y i N|2v2 uvN +λNvS � 3 � i=1 Y i Nvivu + λNvSvN � + 3 � i=1 Y i Nvi � 3 � j=1 Y j NvjvN − λvSvd � +M2 NvN + 3 � i=1 (ANYN)ivivu + ANλNvSvN, ∂Vtree ∂ �νi ��� VEVs as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) = Y i Nvu � 3 � j=1 Y j Nvjvu + λNvSvN � + Y i NvN � 3 � j=1 Y j NvjvN − λvSvd � + 3 � j=1 m2 �Lijvj + (ANYN)ivuvN + g2 1 + g2 2 4 � �v2 d + 3 � j=1 v2 j − v2 u � � vi, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) where m2 �Lij denotes soft-squared masses for sleptons [27, 83–85] and all the concerned parameters are assumed to be real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is apparent from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) that if one neglects terms like Y i NY j N, Y i Nvi for smallness, then vS → 0 suggests vN → 0 and consequently vi → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, a non-zero vS is indirectly connected to a non-zero vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The smallness of vi, compared to vu, vd, also assures that one can still safely use the MSSM relations v2 = v2 u + v2 d and tan β = vu/vd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The presence of tiny but non-zero Y i N, vi, as already stated, generates mixing between left-handed neutrinos and neutral gauginos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These new mixing terms in the EW sector enhance the size of neutral scalar, neutral pseudoscalar, charged scalar, neutral fermion and charged fermion mass matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Being explicit, RP -violating mixing of H0 u, H0 d, S states with � N and three families of �νi, enlarges the NMSSM CP-even and CP-odd neutral scalar mass matrices from 3 × 3 to 7 × 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Similar augmentation appears (i) in the charged scalar sector (2 × 2 in the NMSSM to 8 × 8 due to RP -violating mixing of H± u ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' H∓ d states with the three families of left- and right-handed charged sleptons),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (ii) in the neutral fermion sector (5 × 5 in the NMSSM to 9 × 9 due to RP -violating mixing among neutral gauginos,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' � H0u,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' � H0 d,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �S states with the right-handed neutrino and the three families of left-handed neutrinos),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' and (iii) in the charged fermion sector (2×2 in the NMSSM to 5×5 due to RP - violating mixing among the charged higgsino,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' gaugino states with the three families of the left- and right-handed handed leptons).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, because of tiny values of Y i N, vi, one can easily decompose the aforesaid mass matrices in blocks for approximate analytical studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For example, for all practical purposes, the neutral scalar mass matrix can be decomposed into two diagonal blocks: (i) a 4 × 4 one consisting of CP-even H0 u, H0 d, S, � N states, (ii) another 3 × 3 one consisting of CP-even left-handed sneutrino states, and off-diagonal blocks containing tiny mixing terms between the two aforementioned states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar observation holds true for the neutral pseudoscalar, charged scalar, neutralino and chargino mass matrices, which can be effectively considered as having dimensions 3 × 3, 2 × 2, 6 × 6 – 7 – and 2×2, respectively5, without any loss of generality, leaving the almost pure left-handed CP-odd sneutrino, charged slepton, left-handed neutrino and charged leptons states aside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For the purpose of analyzing the chosen model numerically, it is convenient to express the aforesaid mass matrices in the extended Higgs basis [102–109] which will be introduced subsequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Entries of these mass matrices are detailed in appendix A, along with the full uncoloured scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 A convenient basis choice We have already introduced the tree-level neutral scalar potential in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3), using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, to study the phenomena of PT we need to move beyond the tree- level contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For this purpose, as we already mentioned, it is useful to work in the extended Higgs basis [102–109], given as: Hd = � 1 √ 2(cβHSM − sβHNSM) + i √ 2(−cβG0 + sβANSM) −cβG− + sβH− � , Hu = � sβG+ + cβH+ 1 √ 2(sβHSM + cβHNSM) + i √ 2(sβG0 + cβANSM) � , S = 1 √ 2(HS + iAS), � N = 1 √ 2(NR + i NI), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8) where cβ(sβ) = cos β(sin β) with tan β = vu/vd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that one trades off the scalar, the pseudoscalar and the charged components of the relevant four fields {Hu, Hd, S, � N} with the four neutral CP-even interaction states (HSM, HNSM, HS, NR), three CP-odd interaction states (ANSM, AS, NI), one charged Higgs pairs (H±), along with the neutral and charged Goldstone modes (G0, G±) in the extended Higgs basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This particular basis choice assures the SM-like couplings between HSM with the up-type SM fermions, the down-type SM fermions and the SM vector bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In addition, the aforementioned basis choice also predicts vanishing couplings between HS, NR with the same aforesaid SM states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Furthermore, from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8), in the light of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) and v2 = v2 u + v2 d, one can see that ⟨HSM⟩ = √ 2v, ⟨HNSM⟩ = 0, ⟨HS⟩ = √ 2vS and ⟨NR⟩ = √ 2vN, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', non-vanishing VEVs appear only in certain field directions leaving the SM-direction undisturbed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These interaction states later mix to produce the mass eigenstates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, one of the CP-even states with a mass in the ballpark of 125 GeV (see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [110] and references therein) contains the predominant HSM component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This alignment between the 125 GeV SM-like Higgs in the mass basis and HSM of the extended Higgs basis implies negligible admixing among various states in the extended Higgs basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mathematically, after the EWSB, in the HSM, HNSM, HS, NR basis: |M2 S,1i| ≪ |M2 S,ii − M2 S,11|, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) 5One can easily identify the remaining three neutralinos and three chargions, lying at the bottom of the mass spectrum, as three LH-neutrino dominated states and the charged leptons, e, µ, τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 8 – where i = 2, 3, 4 and M2 S,1i, the entries of the CP-even scalar squared mass matrix, are given in appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is now apparent that in order to satisfy Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) one either needs small M2 S,1i or large |M2 S,ii − M2 S,11|, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', decoupling of HSM from the three remaining states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The latter, in terms of the mass eigenstates, predicts three significantly heavier states dominated by HNSM, HS, NR compositions, and one ∼ O(125 GeV) state controlled by HSM composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In reality, for the SFOEWPT, singlet-like states lighter than 125 GeV are favoured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, heavier singlet-dominated states create a kind of “push-down” effect [71, 111] which makes it difficult to achieve an SM-like Higgs state around 125 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, for our numerical studies, we consider regions of the parameter space that can accommodate one or more singlet-like states lighter than 125 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These light singlet- dominated states are helpful in accommodating a 125 GeV SM-like Higgs through the “push-up effect” [71, 111].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) subsequently to derive a few approximate relations, useful for parameter space scanning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For example, using appendix B and assuming M2 S,11 = m2 h125, the condition M2 S,12 → 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', vanishing mixing between the HSM and HNSM states, implies λ2 ≃ m2 h125 − m2 Z cos 2β 2v2 sin2 β .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10) As mh125, mZ (mass of the SM Z0-boson), v are known, λ approximately appears to be a function of tan β only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar relation like Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10) holds also for the NMSSM [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Applying the same procedure to minimize the mixing between HSM and HS states, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', M2 S,13 → 0, one gets M2 A ≃ 4µ2 sin2 2β � 1 − κ 2λsin 2β + λλNv2 N 4µ2 sin 2β � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) choosing M2 A ≃ 2µ sin 2β � Aλ + κµ λ + λλNv2 N 2µ � 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The last term in the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) appears due to mixing with the RH-sneutrino.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the limit of κ ≪ λ, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11), it turns out that M2 A ≃ M2 H ≃ M2 H± ≃ 4µ2csc2 2β � 1 + λλNv2 N 4µ2 sin 2β � where MH represents mass of a state with dominant HNSM contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The presence of vN shows that these mass eigenstates possess contributions from the RH-sneutrino.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These kinds of mixing may appear sizable depending on λN and vS values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Adopting a similar analysis for M2 S,14 → 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', effacing the mixing between HSM and NR states, it is hardly possible to get a simple relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A light state below 80 GeV with dominant RH-sneutrino contribution hints for a sizable mixing between the HSM and NR states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This effect, via one-loop, makes it easy to assure a 125 GeV SM-like Higgs, even with stop mass below O(1 TeV) [112].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' By choosing the parameters carefully, one can of course consider a heavier stop mass to secure a 125 GeV SM-like Higgs having negligible admixing with a lighter RH-sneutrino-dominated state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This is precisely what we have done while scanning the parameter space since a lighter sneutrino, as also stated earlier, is advantageous for SFOEWPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We will discuss this aspect in detail later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We note in 6At the limit λN → 0, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) reproduces the known NMSSM result [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' If one further considers κ → 0, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) matches the well-known MSSM relation [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 9 – passing that so far we have discussed only the tree-level aspects of the scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In reality, the scalar potential receives considerable contributions from radiative effects involving various SM particles and their SUSY partners [54, 113–115].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Some of these higher-order contributions have observable consequences, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', effects of the top and stop loops to procure a 125 GeV SM-like Higgs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 Higher order contributions It is relevant to investigate various sources critically before implementing higher-order ef- fects arising from the different SM and BSM states on the tree-level scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The effect of higher-order contributions, especially via SUSY partners, is crucial for yielding the observed SM mass spectrum, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', the Higgs mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These effects, however, are diluted for the analysis of EWPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hence, we concentrate only on the leading one-loop effects which can arise from various SM and BSM sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Regarding the latter, one needs to con- sider the following facts: (i) BSM Higgs masses, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', states with dominant HNSM, HS, NR, ANSM, AS and NI components, must not remain very far from the EW scale for a suc- cessful SFOEWPT and, (ii) hitherto unseen experimental evidence of SUSY searches have set lower limits on sparticle masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These limits are stringent for the coloured sector, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', gluinos and squarks, >∼ O (1 TeV) (see, for example, the latest CMS [77–79, 116] and ATLAS [80, 117–119] limits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, for the uncoloured sparticles, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', sleptons, LH-sneutrinos, etc, experimental lower bounds are rather flexible [120–122].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For convenience, however, we consider heavy sleptons and LH-sneutrinos, >∼ O (1 TeV), for this study7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A careful range of relevant parameters was considered so that even with these heavy sleptons one can satisfy the latest result on the anomalous magnetic moment of muon [123] which typically favours the aforesaid states to be lighter than a TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' With the above mentioned facts and assumptions, one ends up with a situation where one encounters >∼ O (1 TeV) sleptons, LH-sneutrinos, squarks & gluinos together with other BSM states, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', scalar and pseudoscalar Higgses, neutralinos, and charginos, in the ballpark of the EW scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Clearly, now one can integrate out these >∼ O (1 TeV) states to yield an effective theory with BSM scalar, pseudoscalar, charged Higgses, neutralinos, charginos and, of course, the SM particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here we would like to point out again that the neutralino and the chargino sector for the concerned model are enhanced compared to the NMSSM, owing to the presence of Y i N in the superpotential (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1)) and non-zero LH-sneutrino VEVs (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, these parameters are compelled to remain tiny (∼ O (10−6 − 10−7) and ∼ O (10���4 − 10−5) GeV), thanks to the constraints arising from the neutrino experiments and the assumption of a TeV scale seesaw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar observation, as already stated, also holds true for the BSM Higgs sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In summary, the effective number of contributing states are four CP-even Higgses (S0 i ), three CP-odd Higgses (P 0 i ), two charged Higgses (H±), six neutralinos (�χ0 i ), two charginos (�χ± i ), charged and the neutral Goldstone bosons (G±, G0), and, the relevant SM particles (t, W ±, Z0)8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This 7Unlike the coloured sector, >∼ O (1 TeV) sleptons and sneutrinos do not introduce large higher-order corrections to the scalar sector owing to small values of the concerned lepton Yukawa couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 8Contributions from the remaining SM fermions are sub-leading due to the sizes of concerned Yukawa couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 10 – set of nineteen particles including the two Goldstone bosons, together with the t, W ±, Z0, will be considered as the dynamical degrees of freedom needed for the current study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can derive parameters of the aforesaid effective theory through the renormalization group equation and subsequently, by matching onto the complete model at some intermediate scale Λ which we fixed at mt, the top mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The leading contribution to the tree-level potential Vtree obtained using this procedure is ∆V = ∆λ2 2 |Hu|4, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12) where ∆λ2 at one-loop level is given by [124–127], ∆λ2 = 3 8π2 y4 t � log � M2 �t m2 t � + A2 t M2 �t � 1 − A2 t 12M2 �t �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13) Here yt is the top Yukawa coupling evaluated using the running top quark mass, M�t = √m�t1m�t2 depicts the geometric mean of two stop masses and At is the soft trilinear coupling between Higgs and stops (appears within L′ soft of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) [27]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can of course write down contributions like the one shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12) for other scalar states, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Hd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Such a term, however, appears due to mixing between Hu and Hd through the effective µ-term and is usually sub-leading compared to the one shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12), as long as µ ≪ M�t 9 and tan β value appears not too large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The quantity ∆λ2 is crucial to accommodate a 125 GeV SM-like Higgs and can be estimated using the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The leftover degrees of freedom also contribute to the potential (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3)) through radiative corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Their collective contributions are given by Coleman-Weinberg po- tential [129] V 1−loop CW = 1 64π2 � i=B,F (−1)Finim4 i (φα) � log �m2 i (φα) Λ2 � − Ci � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14) where i = B (F), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', bosons (fermions), ni represents the relevant degrees of freedom, FB = 0 (FF = 1), Ci is a constant with a value of 3/2 (1/2) for scalars, fermions, longitu- dinally polarized vector bosons (transversely polarized vector bosons), Λ is the aforesaid intermediate energy scale, fixed at mt and, m2 i (φα) = m2 i (HSM, HNSM, HS, NR) denotes field-dependent masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The latter is estimated from Vtree + ∆V (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Contributions from Vtree are detailed in appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The set of involved Bs are given by S0 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='.,4, P 0 1,2,3, H±, G0, G±, Z0, W ± with nB = 4×1, 3×1, 2, 1, 2, 3, 2×3, depend- ing on the nature of the concerned state, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', scalar or complex scalar or massless bosons or massive vector bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar approach for the fermions give F = �χ0 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='.,9, �χ± 4,5, t with nB = 9 × 2, 2 × 2, 3 × 4 considering their electric and colour charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One should note that the presence of G0, G± in the Coleman-Weinberg potential yields divergent contribu- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, these can be effaced by using an infrared regulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, putting all 9Such a choice helps one parameterize radiative contributions from stops effectively, even beyond the one-loop order [125, 127, 128].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 11 – these pieces, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Vtree (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3)), ∆V (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12)) and V 1−loop CW (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14)) together, one obtains the effective scalar potential as Veff = Vtree + V 1−loop CW + ∆V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15) Inclusion of Coleman-Weinberg contributions (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15)) to the tree-level scalar poten- tial, however, changes the position of physical minima and masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' To restore the original position for the physical minima, keeping M2 S,13, M2 S,14 → 0 and maintaining the mass of the CP-even scalar state with leading HSM composition at 125 GeV, one needs to intro- duce appropriate counterterms, encapsulated within another contributor Vct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The latter is normally related to a redefinition of the entries of −Lsoft (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2)) [130–132] which are depicted in appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The counterterms are, thus, not arbitrary but fixed by the aforesaid criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mathematically, ∂ ∂φi � Veff + Vct ���� φi=⟨φi⟩ = 0 and ∂2 ∂φi∂φj � Veff + Vct ���� φi=⟨φj⟩ = 0, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16) with φi = {HSM, HNSM, HS, NR}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can figure out ⟨φi⟩ using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We note in passing that till now we have discussed modifications of the tree-level scalar potential from higher order effects at vanishing temperature, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In reality, however, one also needs to include contributions arising from T ̸= 0 which we will address now.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Contributions from non-zero temperature The one-loop temperature-dependent potential is given by [133] V 1−loop T̸=0 = T 4 2π2 � i=B,F (−1)FiniJB/F �m2 i (φα, T) T 2 � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17) where T represents the temperature, symbols FF,B, nF,B are the same as discussed in the context of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14), m2 i (φα, T) depicts thermal field-dependent masses of the ith degrees of freedom as: m2 i (φα, T) = m2 i (φα) + ciT 2, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18) with ci representing the concerned Daisy coefficients [133–137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These coefficients appear non-vanishing for bosons and are given in appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, JB/F , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', the thermal function, is defined as JB/F � x2 ≡ m2 i (φα, T) T 2 � = ± � ∞ 0 dy y2 log � 1 ∓ e−√ x2+y2� , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19) where + (−) sign is for bosons (fermions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One should note that at the m2 ≫ T 2 limit, where “m” depicts a generic mass term, JB/F suffers an exponential suppression from Boltzmann factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These repressions ensure that massive degrees of freedom, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', squarks, gluinos, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', that are already integrated out (see subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2), do not affect T ̸= 0 corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 12 – Clubbing all the pieces together, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', tree-level scalar potential, one-loop contributions via Coleman-Weinberg potential, and contributions from the finite temperature part, one gets the finite temperature effective scalar potential at the one-loop order as VT = Vtree + ∆V + V ′1−loop CW + Vct + V 1−loop T̸=0 ≡ VT (φ, T), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20) where V ′1−loop CW has a form similar to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14) but replacing m2 i (φα) with thermal masses m2 i (φα, T), as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We will use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20) to inquire about the PT properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We note in passing that the components of VT have explicit gauge dependence [138–140].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, V 1−loop CW (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14)), and hence V ′1−loop CW , also has renormalization scale (Λ) dependence which could dominate over the gauge dependence [141].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' To note, we have worked in the Landau gauge while computing the one-loop corrected potential at both zero and non-zero temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' So far we have discussed different pieces of the scalar potential needed to study the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Now we will address how and to which extent various model parameters can affect the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 3 Choice of parameters The set of new parameters, compared to the NMSSM, are Y i N, λN, vN, (ANYN)i, AλN λN, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3), Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6), and replacing soft-SUSY breaking square mass term M2 N with the corresponding VEV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Now, as already discussed, Y i Ns are associated with the neutrino mass generation through a TeV scale seesaw and thus, are constrained to be small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These Y i N values, for TeV-scale trilinear terms, predicts (ANYN)i ∼ O (10−3 − 10−4) GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The latter is also related to the smallness of vi, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e, the LH-sneutrino VEVs (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6)), as guided by a TeV scale seesaw mechanism and neutrino data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hence, for the PT analysis, we can neglect these tiny parameters, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', vi, Y i N, (ANYN)i, without any loss of generality as they have negligible effects on the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Now from the discussion of section 2, it is evident that relevant “bare” parameters for the uncoloured scalar potential after trading (see appendix E for details) soft-squared masses with the corresponding VEVs (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6)) are, λ, λN, κ, vu, vd, vS, vN, Aλ, Aκ, AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) One can redefine this list further by trading vu, vd with v = � v2u + v2 d, tan β = vu/vd and vS with µ = λvS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As v = 174 GeV is known, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) can be re-casted as λ, λN, κ, tan β, µ, vN, Aλ, Aκ, AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) One can also trade parameter vN with the RH-neutrino mass term MN ∝ λNvN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Similar trading is also possible for Aλ with MA, using a relation given in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We, however, do not use MA, MN for the parameter space scanning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Parameter λ can also be exchanged using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The same parameter can also be constrained using an – 13 – upper-bound on the tree-level SM-like Higgs mass [54, 142, 143], given as m2 Z(cos2 2β + g−2 2 λ2 sin2 2β).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This helps us to consider small tan β ≲ 5 and λ ∼ O(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) or higher such that one gets a significant contribution to the tree-level SM-like Higgs mass10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The ranges of other parameters are also guided by certain aspects, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', in order to avoid the presence of Landau pole [144, 145] below the GUT scale, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', 1016 GeV, one needs to consider λ, κ values carefully at the EW scale such that √ λ2 + κ2 <∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7 [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, smaller values of κ ∼ O(10−2) are favoured as a stronger PT along a particular field direction prefers smaller values of the quartic coupling (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', κ for PT along the HS direction) and larger values of the cubic coupling (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Aκ for a PT along the HS direction), leading to an enhanced barrier height along that specific direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A small value of κ, together with a small Aκ value11, as already discussed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, assure the presence of light CP-even and CP-odd states below 125 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These light states help to procure a 125 GeV SM-like Higgs via the “push-up” [71, 111] effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is evident that one needs to consider Aκ values carefully as for this parameter larger values are favourable for the PT dynamics while smaller ones are useful in fixing the SM-like Higgs mass around 125 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Tree-level mass of the singlet-dominated CP-even state, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), is M2 S,33 ≡ m2 HS = −λλNAλN v2 N 2µ + κAκµ λ + 4κ2µ2 λ2 + λ2v2Aλ sin 2β µ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) This reduces to the known NMSSM result [143] at the limit λN → 0 with a O(λ2) correc- tion12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is apparent from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) that how different parameters appear instrumental in determining the mass of a CP-even singlet-dominated state in this framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We con- sider κ > 0, Ak < 0 in this study to ensure the formation of a barrier along the HS field direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The parameter µ plays a vital role in the PT dynamics and, as given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4), is also crucial for the mass and composition of a singlet-like state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [59] suggests that a strong EWPT favours µ ≲ 300 GeV for the Z3 invariant NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We consider similar ranges for µ in our analysis which also obey the “naturalness” criteria and the LEP chargino bound [148–151], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', |µ| >∼ 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This range of µ values, together with the choice of λ ∼ O(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), suggests a value for vS not too far from the EW scale as required to yield a sizable impact on the EWPT from the singlet sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar observation holds true for the RH-sneutrino VEV vN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The parameter vS also determines the mass term for RH-neutrino, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ∝ λNvS which is constrained to be around a TeV as non-zero neutrino masses in the chosen framework arise through a TeV scale seesaw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The adaptation of a TeV scale seesaw also put some bounds on the parameter λN that is expected to be at most O(1) to avoid the existence of Landau pole below the GUT scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The requirement of having stronger PT along the NR field direction, however, suggests smaller values of λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This behaviour, is similar to κ, as addressed before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The role played by λN in the 10Lower λ values suggest reduced tree-level mass and hence, needs larger corrections from the stop sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the NMSSM, considering the perturbative nature of λ up to the scale of the Grand Unified Theory (GUT) one gets λ ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, in the limit of κ ≪ λ [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 11These ranges of κ, Aκ are guided by the well-known U(1)PQ, U(1)R limits [143, 146, 147] for the NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 12This term appear to be sub-leading for small λ, tan β values together with vS ≪ v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 14 – PT dynamics is somewhat non-trivial and will be addressed later in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The remaining parameters, Aλ, AλN are connected to the scale of vS, vN and thus, are expected to be in the ballpark of a TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These parameters, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Aλ, AλN also affect tree-level masses of the CP-even and CP-odd scalar states as detailed in appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this analysis we consider Aλ > 0 and AλN < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The latter choice helps to efface the possible existence of a tachyonic state in the CP-odd scalar sector (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We note in passing that so far we have presented a qualitative discussion in the context of the chosen independent parameters, as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For finding BPs through numerical analysis, one, however, also needs to consider all the relevant present and anticipated experimental bounds which we will address in the next subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 Experimental Constraints A viable phenomenological analysis must satisfy all the concerned experimental limits, the existing and the projected ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The inclusion of these bounds reduces the size of the available parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this analysis, apart from considering sensitivity reaches of the existing [152–154] and upcoming [81, 155, 156] GW detection setups, we also consid- ered constraints arising from (i) analysis of the SM-like Higgs boson properties and BSM Higgs searches at colliders, (ii) other BSM searches at the colliders, (iii) flavour-violating processes, (iv) neutrino experiments, (v) muon anomalous magnetic moment, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In order to employ these constraints in our numerical analysis, we first implemented the concerned model in SARAH 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 [157–164].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Subsequently, we use SPheno-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 [158, 162, 164–171] to get the mass spectrum and decay widths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The output of SPheno-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 also provides branching fractions for various flavour-violating processes, BSM contributions to the muon anomalous magnetic moment [166], several LHC observables like reduced Higgs couplings, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We will now discuss the aforesaid constraints one by one in further detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (i) Analysis of the SM-like Higgs boson properties and BSM Higgs searches at colliders: Here one needs to consider two aspects: (a) SM-like Higgs analyses, and (b) the BSM Higgs searches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Concerning the first, important constraints appear from the measured mass, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ≈ 125 GeV [42, 172], and couplings [39–42, 173–177].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have used these results to assure the existence of an SM-like 125 GeV Higgs in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, to assure the SM- like nature we also put a lower limit (80%) on the Hu composition of the 125 GeV mass eigenstate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Regarding the BSM Higgs searches, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', for states with leading HNSM, HS components, and the charged Higgs, we consider the concerned experimental bounds, see for example Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [178] and references therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We used HiggsBounds [179] 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 [180] to implement experimental constraints from the SM and BSM Higgs searches in our numerical study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (ii) Other BSM searches at the colliders: We already discussed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 that we are working in an effective framework after integrating out heavy degrees of freedom like gluinos, squarks and even charged sleptons and LH-sneutrinos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We consider these states to remain heavier than 1 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Such assumptions, especially for gluinos and squarks are supported by the experimental findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this study, we consider gluino mass >∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 TeV and squark masses >∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These choices are guided by the present CMS [77–79, 116] and ATLAS [80, 117–119] observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Experimental lower bounds on the charged slepton – 15 – and LH-sneutrino masses are somewhat less [120–122].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, we also considered them to be heavier than a TeV and integrate them out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In our numerical study, the lightest neutralino mass varies from 3 GeV to 120 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, this does not contradict any experimental bounds, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', SM-like Higgs decaying to a pair of neutralinos, (see for example Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [80, 121, 181–184]) as its predominant composition (≳ 90%) is from the singlino and the RH-neutrino.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For charginos, we used a lower bound of 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 GeV [148–151] in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is important to note that experimental lower bounds are often interpreted in the context of simplified models and hence, they may not directly restrict the concerned model parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (iii) Flavour-violating processes: The presence of BSM states can significantly enhance branching fractions (BR) of certain flavour-violating processes, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', B → Xsγ, B0 s → µ+µ− (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [185–191] and references therein), etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', compared to the SM predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can minimize these new contributions by taking tan β <∼ 5 and fixing squarks, gluinos, sleptons, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', masses to be heavier than a TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, finite BSM contributions to these pro- cesses still appear through the EW scale uncoloured neutral scalars, neutral pseudoscalars, charged scalars, charginos and neutralinos, as required for the EWPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, we consider the following 2σ bounds BR(B → Xsγ) = (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='49 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='38) × 10−4, BR(B0 s → µ+µ−) = (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='45 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='58) × 10−9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) We note in passing that BR(B → Xsγ), BR(B0 s → µ+µ−) also receive extra contributions due to R-parity breaking [192, 193].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, given the framework of a TeV scale seesaw, the size of R-parity violating couplings, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Y i NvN, appears to be ∼ O(10−3 − 10−4) GeV and hence, hardly yield any significant contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We consider charged Yukawa couplings to be diagonal for this work which helps to bypass constraints from the flavour-violating Higgs decays [194, 195].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can also con- sider slepton soft squared masses to be diagonal to minimize mixing among sleptons (both charged and neutral).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' With these choices, the effective bilinear R-parity violating cou- plings, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Y i NvN, and the LH-sneutrino VEVs appear to be main sources for the various charged lepton flavour violating (cLFV) processes like µ → eγ, µ → eee, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, the scale of these couplings, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ∼ O(10−3 − 10−4) GeV, as required for a TeV scale seesaw, can easily evade these bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This behaviour is very similar to the SUSY models with bilinear R-parity violation [196–198].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We note in passing that in our numerical studies we emphasized on the cLFV processes for the µ over the similar ones from τ as the con- cerned existing and upcoming experimental sensitivities are much more stringent for µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, we also include constraints for cLFV processes involving a τ in our analysis, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', BR(τ → µγ) < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 × 10−8 [199].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The µ-based cLFV bounds included in the current analysis are given by BR(µ → eγ) < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 × 10−13 [200], BR(µ → eee) < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 × 10−12 [201], CR(µN → eN∗) < 7 × 10−13 [202], – 16 – where CR(µN → eN∗) represents muon to electron conversion ratio in atomic nuclei with N (N∗) representing the nucleus in the normal (excited) state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The given number, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', 7 × 10−13 is for the gold nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (iv) Neutrino experiments: With one generation of RH-neutrino, as already stated in section 2, it is not possible to accommodate the experimentally observed three-flavour neu- trino masses and mixing [47, 48, 53], even with the inclusion of loop effects [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, one will get one massive and two nearly massless neutrinos in this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, even in such a scenario, we used constraints from the atmospheric mass squared difference ∆m2 atm, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='430(−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='574) × 10−3 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='593(−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='410) × 10−3 eV2 for normal (inverted) hierarchy, and the sum of three neutrino masses ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 eV [1, 203].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (v) Muon anomalous magnetic moment: Just like the flavour violating processes, the anomalous magnetic moment of muon also receives extra contributions over the SM from new parameters and the BSM states (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [204, 205] and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The recent comprehensive SM prediction of the muon anomaly is 116591810 (43) × 10−11 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='37 ppm) [206] while the experimental average13 is 116592061(41) × 10−11 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='35 ppm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These numbers, adding errors in quadrature, gives ∆aµ = (251±59)×10−11 which is arising from the BSM sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This, in 4σ span, gives (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 − 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) × 10−10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The BSM contributions, especially involving charged sleptons states below a TeV [208–210], can affect this process significantly and can easily accommodate the latest experimental observation [123].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In our analysis, as already discussed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, we kept charged slepton masses around a TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, by playing with the other concerned parameters we checked that the aforesaid ∆aµ range, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 − 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) × 10−10 is not violated in our BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, the choice of slepton, squark masses around a TeV or more yields suppressed cLFV processes and smaller BSM contributions to the anomalous magnetic moment of the muon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' All the chosen BPs respect all the five aforesaid classes of constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We now discuss this study’s key objectives in detail, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', PT properties and GW production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 4 The EWPT and its Properties As we already discussed, understanding the EWPT properties in the early Universe in a Particle Physics model has twofold advantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Firstly, it can be confirmed whether the model carries the prospect to explain the origin of EWBG at some corner of the parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Secondly, it provides scope to test the model at GW detectors beyond the conventional BSM searches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One of the prerequisites of EWBG is the FOPT with sufficient strength along the SU(2)L field directions so that it can suppress the processes which wash out the baryon asymmetry after it is produced, namely SU(2)L sphalerons [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The same FOPT may yield a detectable amount of GWs that could be accessible by future GW interferometers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The structure of the thermal effective potential for a PT reveals that at very high temperatures the Universe would be in a symmetric phase with the relevant field (say φi) being located at zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As the Universe cools down, the symmetric vacuum may disappear 13Here we have used combined experimental average obtained from the FNAL [123] and the BNL E821 [207] results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 17 – and the corresponding field values could be finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Additionally, a second minimum can be formed at some higher field value which becomes degenerate with the previous one at T = Tc, known as critical temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At temperature below Tc, the transition from the high-T VEVs (say v′ X) to the low-T VEVs (say vX) can take place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here X = u, d, S, i, N as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We should note here that a high-T (low-T) phase means an unstable (stable) vacuum below Tc or above nucleation temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Therefore, to have an in-depth understanding of PT dynamics, an estimate of critical temperature Tc and the strength of PT are enormously important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Theoretically, the critical temperature can be obtained from the following equality: VT (v′ X, Tc) = VT (vX, Tc), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where v′ X and vX represent high-T and low-T VEVs, respectively, along a particular field direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We also need to ensure the existence of high- and low-T vacua which can be confirmed by the following equalities, ∂φαVT (v′ X, Tc) = 0, ∂φαVT (vX, Tc) = 0, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) where φα = {HSM, HNSM, HS, NR}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In many cases, including ours, analytical solutions of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) are almost impossible to derive in order to obtain the estimates of the relevant parameters to study the PT properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have used the publicly available package cosmoTransitions [211] to carry out the numerical calculation for our model in consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A FOPT proceeds via bubble nucleation and the nucleation rate (Γ) per unit volume (V ) at finite temperature is given by Γ V ∝ T 4e−SE/T , where SE is the three-dimensional effective Euclidean action known as bounce action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The criterion which set the condition for the onset of bubble nucleation is given by [16, 212], SE(Tn) Tn ≃ 140, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) where Tn is the nucleation temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' If it happens that the quantity SE(Tn) Tn > 140, then the transition does not occur due to low tunnelling probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As mentioned earlier, we use cosmoTransitions [211] to compute SE and Tn, which also allows for estimating the probability of a transition taking place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Since we have four- dimensional field space, relevant to EWPT, a detailed scan of the model parameter space is challenging and numerically expensive as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Therefore in the present work, we first provide a representative BP-based study which will be detailed subsequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We will see that such BPs are sufficient to understand the parameter space of NMSSM + one RHN framework that can potentially give rise to an SFOPT and can also be interesting from the viewpoint of EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Subsequently, we discuss the impact of new parameters in the present setup compared to the NMSSM on PT strength along different field directions by providing a scan of the relevant parameter spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Before we proceed further, let us now define different criteria to consider a PT to be a strong one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Conventionally, in the critical temperature analysis, the order parameter that – 18 – decides the fate of PT is given by, γc ≡ vc(Tc) Tc = � ⟨HSM⟩2 + ⟨HNSM⟩2 Tc ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) where vc(Tc) denotes VEVs of the SU(2)L Higgs fields, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', HSM, HNSM, at Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For the nu- cleation temperature calculation, we define an SFOPT along the respective field directions as follows: Along SU(2)L doublet Higgs direction: ∆φSU(2) Tn = � ( � HlT SM � − � HhT SM � )2 + ( � HlT NSM � − � HhT NSM � )2 Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) Along the SU(2)L singlet Higgs and the RH-sneutrino direction: ∆φS Tn = � ( � HlT S � − � HhT S � )2 Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' ∆φ � N Tn = � ( � NlT R � − � NhT R � )2 Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) where ∆φSU(2) Tn , ∆φS Tn and ∆φ � N Tn represent PT strength along the SU(2)L-doublet, SU(2)L- singlet and the RH-sneutrino field direction, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The notation, � ΦlT� denotes the low temperature minimum while � ΦhT� is the high temperature minimum of a scalar field (Φ) before nucleation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A favourable condition to yield the observed baryon asymmetry of the Universe via the EWBG is ( � HhT SM � , � HhT NSM � ) = (0, 0) with ∆φSU(2) Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In con- trast, when ( � HhT SM � , � HhT NSM � ) ̸= (0, 0), the sphaleron processes outside the bubble gets substantially suppressed which lead to inefficient production of the baryon asymmetry of the Universe from the EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 PT in the NMSSM + one RHN model As we already specified, the field space relevant to the PT analysis is four-dimensional in the present framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This opens up the possibility of obtaining a richer PT pattern compared to the case of the NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We define the high-temperature symmetric vacuum of the scalar potential as Ω0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In principle, one can have many distinct PT patterns in the whole parameter region of the NMSSM + one RHN framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here we summarise a few such possibilities that advocate some unique PT patterns along the various field directions: Type-I: As already stated, at T ≫ Tc, the Universe remains in the symmetric phase where each of the four fields has zero VEV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The simplest possibility for a PT is that at critical temperature the symmetry-breaking minimum of the total scalar potential appears only along the HSM direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Then the PT happens from symmetric to the broken phase directly in that direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We denote this by Ω0 PT −−→ ΩHSM where ΩHSM represents the vacuum along SM Higgs direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Type-IIa: This pattern involves displacement of the HS field VEV (at T > Tc) from the initial zero value as the Universe cools down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We label it as Type II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Below Tc, the PT occurs along both the HSM and HS field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We denote this particular pattern (IIa) as Ω0 → Ω′ HS PT −−→ ΩHSM + ΩHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 19 – Type-IIb: This is similar to the earlier case where for T > Tc, a shift of the HS field value from zero vacuum appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Below the critical temperature, the transition also takes place along the HS direction only and is represented by Ω0 → Ω′ HS PT −−→ ΩHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Type-IIc: This case also falls under the Type II category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, below critical temperature, the PT happens along both HS and NR field directions as indicated by Ω0 → Ω′ HS PT −−→ ΩHS + ΩNR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Type-IIIa: In this category, for T > Tc, the shifts of HSM and HS VEVs from the initial zero values take place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' When T < Tc, PT also occurs along the same field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This pattern is represented by Ω0 → Ω′ HSM + Ω′ HS PT −−→ ΩHSM+ΩHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Type-IIIb: In this category, at T > Tc, the behaviour of the scalar potential is similar to the last one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, at T < Tc, the PT occurs along HSM, HS and NR directions as indicated by Ω0 → Ω′ HSM + Ω′ HS PT −−→ ΩHSM +ΩHS+ΩNR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Type-IV: This category is defined to indicate a particular PT pattern where at a T > Tc, the symmetric vacuum of the total scalar potential gets displaced along the S and NR field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The PT occurs below Tc along any of the four field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As described earlier, any BP showing either of the type-I or type-IIa PT pattern is preferred in view of efficient EWBG, provided the corresponding PT strength satisfies the condition ∆φSU(2) Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Whereas, the rest of the types as listed above may not lead to EWBG due to non-satisfaction of either of the conditions, �� HhT SM � , � HhT NSM �� ̸= (0, 0) or ∆φSU(2) Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The PT types that do not favour EWBG, can be still interesting if it triggers an SFOPT along the SU(2)L doublet or singlet field directions and subsequently radiates GW at a detectable amount.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 Numerical Results As earlier mentioned, we would like to begin with a benchmark-based study of EWPT in the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the later part, we will be discussing explicitly the dependence of new parameters in the current setup compared to the NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We first tabulate six BPs in Table 1 that are consistent with all relevant theoretical and experimental constraints, as discussed in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We select the BPs in such a way that they show distinct PT characteristics with some of them favouring EWBG and carrying good to moderate detec- tion prospects at GW detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that we have four soft-SUSY breaking parameters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Aλ, Aκ, AλN , AN) in our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We discuss the possible role of all the A− parameters in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Recall that one of the soft parameters AN does not contribute much to the PT dynamics since it is always associated with the tiny neutrino Yukawa coupling Y i N as earlier clarified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We keep AN above the TeV scale for all BPs, which ensures slepton masses ≳ O(1 TeV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Table 1, we provide the eigenvalues of the four CP-even mass eigenstates, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', mh125, mH, mHS, m � N, corresponding to each BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The leading composition in these states are coming from the HSM, HNSM, HS and NR fields, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have explicitly – 20 – checked that all the BPs evade the relevant experimental bounds as detailed in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, we have explicitly shown values of the various flavour-violating processes ∆aµ and ∆m2 atm for the sake of completeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Table 2 and Table 3, we have summarised the PT outputs of the BPs as obtained from the cosmoTransitions [211] package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Below we discuss the PT characteristics for each of the BPs in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-I BP-II BP-III BP-IV BP-V BP-VI tan β 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='90 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='74 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='90 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='77 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='79 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='86 λ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='416 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='412 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='416 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='384 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='118 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='111 κ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='022 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='019 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='022 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='013 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='051 λN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='146 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='142 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='146 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='130 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='260 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='238 Y 1 N × 107 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Y 2 N × 107 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Y 3 N × 107 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Aλ [GeV] 775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='48 705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='32 775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='48 1184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='87 988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 920.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 Aκ [GeV] 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='75 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='37 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='70 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 AλN [GeV] 349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='68 337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='77 326.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='60 363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 1358.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='30 1528.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='57 AN [GeV] 16000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 12000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 8500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 12000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 6500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 5000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 µ [GeV] 224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='56 220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='86 224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='56 203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='59 162.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='64 vN [GeV] 308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='80 325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='21 284.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='50 386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='45 136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='57 355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='66 v1 × 104 [GeV] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='55 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 v2 × 104 [GeV] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='55 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 v3 × 104 [GeV] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='55 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 mh125 [GeV] 126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='02 124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='80 125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='64 125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='63 126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='28 124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='05 mH [GeV] 772.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='36 718.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='07 772.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='73 1213.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='76 897.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='40 1012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 mHS [GeV] 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='60 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='98 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='48 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='54 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='31 195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='41 m � N [GeV] 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='60 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='89 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='63 BR(B → Xsγ) × 104 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='70 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='62 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='47 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='59 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='55 BR(B0 s → µ+µ−) × 109 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='26 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19 BR(µ → eγ) × 1030 394 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='98 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 404 173 BR(µ → eee) × 1029 113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='04 CR(µN → eN∗) × 1028 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='81 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='49 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='43 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='85 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='31 ∆m2 atm × 103 eV2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='51 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='57 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='58 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='54 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='58 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='46 ∆aµ × 1010 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='88 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='75 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='42 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='94 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='54 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The representative BPs that we will use to study the PT patterns in the present framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Apart from the parameters mentioned above, we fix the gaugino mass parameters M1 = 300 GeV, M2 = 2M1, M3 = 6M1, trilinear soft coupling At around 2 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We also consider RH-slepton soft masses above 1 TeV and squarks soft masses M � Qi, M�uc i , M � dc i all above 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' With the chosen values of parameters Y i N, vi and AN, the LH-sneutrino and LH-slepton masses also appear in the ballpark of a TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As already stated in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, suppressed cLFV processes and smaller BSM contributions to the anomalous magnetic moment of muon are evident now due to slepton, squark masses around a TeV or more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, for BP-II, ∆aµ remains below the aforesaid 4σ range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' CR(µ N → e N ∗) value is estimated for the gold nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-I and BP-II : Out of these two representative BPs, BP-I shows an SFOPT along both the SU(2)L-doublet and singlet field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, we obtain a weaker FOPT for BP-II in the SU(2)L doublet directions whereas a stronger one along the SU(2)L singlet direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Figure 1, we have shown the evolution of the phase structures along the HSM (left) and the HS (right) field directions as a function of temperature for BP-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The critical temperature for BP-I is 117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 GeV as noted in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Above the critical – 21 – BP-I BP-II BP-III Transition Type Type-IIa Type-IIa Type-IIIa vc/Tc 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='30 (In);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0 (Out) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='73 (I);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0 (O) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='83 (I);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 (O) ∆φSU(2)/Tn 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='58 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='81 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='28 ∆φS/Tn 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='70 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 ∆φ � N/Tn 0 0 0 Tc (GeV) 117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 Tn (GeV) 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 high-Tn VEVs (0, 0, 113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8, 0) (0, 0, 341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 0) (105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8, 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5, 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8, 0) low-Tn VEVs (173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5, 631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3, 0) (102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3, 488.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, 0) (208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8, 719.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, 0) high-Tc VEVs (0, 0, 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 0) (0, 0, 333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, 0) (62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 0) low-Tc VEVs (152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8, 572.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5, 0) (92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, 467.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, 0) (186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 625.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4, 0) Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The PT properties for first three BPs as tabulated in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' temperature HSM is located at zero (as pointed by the legend phase 3, red coloured, in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At T = Tc, we find another degenerate minimum along the same field direction, which is ⟨HSM⟩ = 152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 GeV (as marked by phase 2, green coloured).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The black coloured line with the arrow connects the high-T and low-T VEVs indicating a possible FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The bubble nucleation occurs afterwards and it ends at 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 GeV which we have highlighted in orange colour (also labelled as phase 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar pattern can be observed along HS direction too as shown in the right panel of Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The interesting point to mention here is that the ⟨HS⟩ starts to get displaced from zero value even at a temperature above Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This is in contrast to the evolution of phase structure along HSM direction for this particular BP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The BP-II shows similar characteristics although the strong PT occurs only along the HS direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The high-temperature behaviour of the total scalar potential leads us to identify the PT properties for both BP-I and BP-II as Type-IIa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For BP-I, we observe from Table 2, that the PT strength at T = Tc is greater than one inside the bubble and zero outside the bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Therefore a baryon number may be generated in the broken phase and the wash-out effects are likely to be suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In view of this, BP-I is favoured in order to address EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, BP-II shows a weaker FOPT in the SU(2)L doublet directions and hence is not suitable to address the question of EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In subsection 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 we will discuss the strength of emitted GW spectrum during bubble nucleation for both BP-I and BP-II in view of the proposed sensitivities of a few forthcoming GW experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-III: The BP-III falls into Type-IIIa category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It implies that at a temperature above Tc, both HSM and HS attain non-zero VEVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The critical temperature for this BP comes out to be 101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At this temperature, the presence of two degenerate vacua is noticed having nonzero field values for both SU(2)L doublet and singlet fields, which set the possibility of a PT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We obtain SFOPT along both the SU(2)L-doublet and singlet field directions where the PT strength turns out to be larger than one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, the quantity φc Tc becomes non-zero both inside and outside the bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This gives rise to a stronger wash- out effect which is likely to suppress the yield of baryon asymmetry and hence seemingly disfavored in view of EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, it carries good detection prospects in the GW detectors due to relatively larger PT strength ∆φS Tn compared to BP-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 22 – 0 50 100 150 200 250 ⟨HSM⟩ [GeV] 0 50 100 150 200 250 300 T [GeV] phase3 phase2 phase1 phase0 0 200 400 600 800 ⟨HS⟩ [GeV] 0 50 100 150 200 250 300 T [GeV] phase3 phase2 phase1 phase0 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phase structures as a function of temperature along the HSM and HS field directions for BP-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Different colours represent the locations of a particular field as a function of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The black coloured line with the arrow connects two degenerate phases at T = Tc and the direction of the arrow indicates a possible FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0 200 400 600 ⟨HS⟩ [GeV] 0 200 400 600 800 1000 T [GeV] phase3 phase2 phase1 phase0 −500 −400 −300 −200 −100 0 ⟨NR⟩ [GeV] 0 200 400 600 800 1000 T [GeV] phase3 phase2 phase1 phase0 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phase structures as function of temperature along HS and NR field directions for BP-IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Different colours show the evolution of minimum along a particular field direction with temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The line with the arrow connects two degenerate phases at T = Tc and the direction of the arrow indicates a possible FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-IV: The BP-IV in Table 1 shows type-IIc PT pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The numerical estimates of the relevant parameters that govern the PT dynamics for BP-IV are listed in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We find SOFPT along both the HS and NR directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Clearly, this BP is not preferred to address EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Figure 2, we show the phase structure along HS and NR directions for BP-IV as a function of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At temperature above Tc = 184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 GeV, HS takes a non-zero field value which is the typical type-II feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The black coloured line with arrow in Figure 2 connects two degenerate phases at the critical temperature and paves the way for the PTs in the respective singlet field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-V: This BP is unique in the sense that we obtain FOPT below the critical tempera- ture along the directions of SU(2)L fields, HS and NR at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This BP falls into – 23 – the type-III category since at temperature above Tc, we find high-T VEV to be non-zero for both HSM and HS fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Although this particular BP shows FOPT along HSM direction, the strength is relatively weaker as can be seen from Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Therefore, the possibility of EWBG remains unlikely for this BP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, we obtain SFOPT along HS and ˜N directions in contrast to weaker FOPT in the HSM direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-IV BP-V BP-VI Transition Type Type-IIc Type-IIIb Type-IV vc/Tc 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (In) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (Out) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (I);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (O) 2nd: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='54 (In);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (Out) 1st: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (In) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (Out) ∆φSU(2)/Tn 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='04 1st: 0 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2nd: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='57 ∆φS/Tn 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='56 1st: 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2nd: 0 ∆φ � N/Tn 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='81 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='71 1st: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2nd: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13 Tc (GeV) 184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 177.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 2nd: 206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 1st: 232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 Tn (GeV) 165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 2nd: 204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 1st: 232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 high-Tn VEVs (0, 0, 529.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 0) (137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5, 1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 0) 2nd: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, −720.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) 1st: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, −845.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) low-Tn VEVs (0, 0, 696.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, −465.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='28) (143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, 0, 1832.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, 247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) 2nd: (117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, 0, 2088.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, −747.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) 1st: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, -807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) high-Tc VEVs (0, 0, 459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 0) (0, 0, 1484.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 0) 2nd: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, −724.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) 1st: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, −846.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) low-Tc VEVs (0, 0, 671.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, −429.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) (0, 0, 1827.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) 2nd: (112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3, 0, 2088.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, −749.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) 1st: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4, −808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The PT properties for the last three BPs as tabulated in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-VI: So far, for all the BPs we have obtained single-step FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In contrast, BP-VI shows a two-step FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The outputs are tabulated in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In both steps, the high- temperature behaviour of the scalar potential closely follows the Type-IV pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, in the first step FOPT occurs along the NR direction only, while in the second step, we find FOPT in both the NR and HSM directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that, this BP shows a weaker FOPT and hence, is not suitable for the EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Recall from section 3 that the new physics parameters, relevant for the study of PT in the current framework are {λN, AλN , vN} compared to the Z3 symmetric NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the subsequent analysis, we like to inquire about the impact of these new parameters on the PT strength along different field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Also, note that a FOPT apparently favours a lighter RH-sneutrino-like state below 125 GeV as we observe from the BP-based study of PT and their outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This characteristic is likely to be further confirmed while we vary the new parameters and obtain the sensitivity of PT strength on these parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' First, in Figure 3 we show the impact of vN (left) and λN (right) on the PT strength vc Tc .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In each of the sub-figures, we have fixed the other relevant parameters as in BP-I of Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We find the PT strength decreases with the rise of both vN and λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We repeat the analysis for the same BP as shown in the top panel of Figure 4 considering nucleation temperature calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In particular, we estimate the PT strength in the SU(2)L field – 24 – 150 200 250 300 350 400 vN (GeV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 vc/Tc 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='26 λN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 vc/Tc Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These plots show the dependence of PT strength on vN (left) and λN (right) in the Tc calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Parameters Y i N, vi and AN have no significant effect in PT dynamics and thus, we keep their values ∼ O(10−7), ∼ O(10−4 GeV), ∼ O(1 TeV), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Other relevant parameters are fixed as in BP-I of Table 1, except vN and λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' directions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ∆φSU(2)/Tn as function of vN and λN and notice similar trends as in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Now a smaller λN or vN implies lighter sneutrino following the CP-even mass matrices mentioned in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hence, Figures 3 and 4 further reinforce the fact that a comparatively lighter RH-snuetrino is indeed preferred to trigger a possible FOPT along the SU(2)L doublet field directions in the present framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Now the remaining new parameter AλN is expected to show a minor impact on the ∆φSU(2)/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This is because it is not directly connected to the relevant terms at the tree level in the Lagrangian involving the SU(2) doublet Higgs fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Indeed, in our analysis, we have found that the ∆φSU(2)/Tn remains more or less unaltered upon varying AλN as shown in the bottom panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Next, we like to examine the impact of the new physics parameters as earlier specified on the PT strength along SU(2)L-singlet field direction ∆φS/Tn while the other parameters are set according to BP-III of Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In top panel of Figure 5 we depict the variation of ∆φS/Tn as function of vN (left) and λN (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We observe that the quantity ∆φS/Tn increases upon lowering λN when vN is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the other case when we fix λN and vary vN, the ∆φS/Tn gets enhanced for a smaller vN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Once again, these observations further strengthen our earlier finding that a lighter RH-sneutrino below 125 GeV is favoured for the occurrence of an SFOPT in the SU(2)L-singlet, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', HS direction as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, we also notice that the ∆φS/Tn increases with the rise of AλN as shown in the bottom panel of Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that AλN is appearing as the coefficient of the cubic interaction S � N � N (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hence a larger AλN is expected to increase the barrier height which results in a stronger ∆φS/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Previously, we have found that BP-IV provides us with a SOFPT along the NR field direction ∆φ � N/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We would like to utilize this particular BP to enquire about the de- pendence of new parameters on ∆φ � N/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In top left of Figure 6, we show the dependence of ∆φ � N/Tn on vN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We find that for vN ≲ 500 GeV, the ∆φ � N/Tn remains more or less – 25 – 320 340 360 380 400 vN (GeV) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 ∆φSU(2)/Tn 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='26 λN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 ∆φSU(2)/Tn −1400 −1200 −1000 −800 −600 −400 −200 AλN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='09 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 ∆φSU(2)/Tn Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These plots show the dependence of PT strength ∆φSU(2)/Tn on vN (top left), λN (top right) and AλN (bottom) along the SU(2)L field direction, in the Tn calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here, orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed as in BP-I of Table 1, except vN, λN and AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' constant, however, decreases while we increase vN further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Additionally, from top right of Figure 6 the ∆φ � N/Tn gets reduced as well upon increasing λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The reason for this is twofold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As we mentioned earlier, a smaller λN leads to lighter RH-sneutrino states below 125 GeV which in turn enhances the ∆φ � N/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moreover, a smaller λN also assists in increasing the barrier height and hence results in enhanced ∆φ � N/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In bottom panel of Figure 6, we have shown the ∆φ � N/Tn strength gets enhanced upon increasing AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This is once again caused by the enhanced barrier height for a larger AλN similar to the earlier case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' After examining the individual dependence of new parameters on PT strength, we now give a random scan on new physics parameters highlighting the region allowed by the experimental constraints and favouring an SFOPT along SU(2)L field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We vary (λN, vN) and fix the other relevant parameters in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) following BP-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, orders of parameters Y i N, vi and AN are chosen as ∼ O(10−7), ∼ O(10−4 GeV), ∼ O(1 – 26 – 150 200 250 300 350 400 vN (GeV) 2 3 4 5 6 ∆φS/Tn 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='26 λN 1 2 3 4 5 ∆φS/Tn −800 −700 −600 −500 −400 −300 −200 AλN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 ∆φS/Tn Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These plots show the dependence of PT strength ∆φS/Tn on vN (top left), λN (top right) and AλN (bottom) along the SU(2)L-singlet field direction, in the Tn calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here, orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed as in BP-III of Table 1, except vN, λN and AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' TeV), respectively, as they hardly affect the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have randomly generated pairs of (λN, vN) and pass through all the experimental bounds mentioned in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We first sort out the points that pass all the experimental constraints as shown in green colour in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Next, we apply the condition of SFOPT along the SU(2)L field direction and pin down the points that favour SFOPT only and SFOPT with possible EWBG having minimal wash-out effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have marked them in Figure 7 by coloured ‘▲’ and ‘■’, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These points depict the variation of ∆φSU(2)/Tn in the vN - λN plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Next in Figure 8, we made a scenario similar to that of Figure 7, however, in the HS field direction in the context of BP-IV, as shown in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here, points which undergo SFOPT are marked by ‘⋆’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We also compute the ∆φS/Tn strength and find that the ∆φS/Tn strength is maximum when both λN and vN are small, which is in agreement with our earlier observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 27 – 400 500 600 700 800 900 1000 vN (GeV) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 ∆φ� N/Tn 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='35 λN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 ∆φ� N/Tn −1000 −800 −600 −400 −200 AλN 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 ∆φ� N/Tn Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These plots show the dependence of PT strength ∆φ � N/Tn on vN (top left), on λN (top right) and on AλN (bottom) along the NR direction, in the Tn calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here, orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed as in BP-IV of Table 1, except vN, λN and AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, in Figure 9 we perform an analogous exercise to show the variation of ∆φ � N/Tn in the vN - λN plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this case, we have utilized the BP-IV of Table 3 once again to fix the other relevant parameters, except vN and λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The green-coloured points are allowed by the various experimental constraints as stated in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We mark the points that favour SFOPT in the NR direction by coloured ‘⋆’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Once again, we find that the ∆φ � N/Tn is maximum for simultaneous lower values of vN and λN, consistent with our earlier findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 GW spectrum from SFOPT in the NMSSM + one RHN model A cosmological FOPT can produce GWs in the early Universe that contains information about the strength of different model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the preceding section, we have dis- cussed different PT characteristics in the proposed framework and computed the relevant quantities that determine the strength of a PT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the current section, we will be talking – 28 – 220 240 260 280 300 320 340 vN (GeV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='135 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='140 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='145 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='155 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='160 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='165 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='170 λN tan β = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='90, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='416, κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='022, µ = 224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='56 GeV, Aλ = 775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='48 GeV, Aκ = −62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='75 GeV, AλN = −349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='68 GeV Allowed by experimental bounds SFOPT and no EWBG SFOPT and possible EWBG 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='50 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='75 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='00 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='25 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='50 ∆φSU(2)/Tn Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This figure shows variations of ∆φSU(2)/Tn in the vN - λN plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The green-coloured points pass all the experimental constraints as discussed in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The points favoured for SFOPT along the SU(2)L field direction without and with EWBG are marked by coloured ‘▲’ and ‘■’ symbols, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed as in BP-I of Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' about the production of GW and its detection prospects within our model setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As we have mentioned earlier, a FOPT is characterized by critical temperature Tc, and nucleation temperature Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The critical temperature indicates the moment when the location of the global minimum changes from one vacuum phase to another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, the critical temperature analysis does not assure that the associated PT is indeed taking place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, FOPT proceeds via bubble nucleation, and hence calculation of nucleation temperature is very crucial in order to obtain the phenomenological parameters that are important from the standpoint of estimating GW spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' When the nucleation happens, at a temperature below Tc, the probability of tunnelling Γ(T) from the false vacuum to the true one is given by [213], Γ(T) ≈ T 4 � SE 2πT �3/2 e− SE T , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) where SE is the bounce action corresponding to the critical bubble and can be written as [212], SE = � ∞ 0 4πr2dr � VT (φ, T) + 1 2 �dφ(r) dr �2� , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8) with r being the radial coordinate and φ corresponding to the scalar dynamical fields present in a model framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The scalar field solution φ can be derived by solving the – 29 – 340 360 380 400 420 440 460 vN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 λN tan β = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='77, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='384, κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='012, µ = 203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 GeV, Aλ = 1184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='87 GeV, Aκ = −107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 GeV, AλN = −363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 GeV Allowed by experimental bounds SFOPT along HS direction 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 ∆φS/Tn Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This figure shows variations of ∆φS/Tn in the vN - λN plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The green-coloured points pass all the experimental constraints as discussed in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The points favoured for SFOPT along the HS field direction are marked by coloured ‘⋆’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed following BP-IV of Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' classical field equation [212, 214, 215] d2φ dr2 + 2 r dφ dr = dVT (φ, T) dr , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) and subsequently applying proper boundary conditions: dφ dr = 0 when r → 0 and φ(r) → φfalse when r → ∞, where φfalse represents the four-dimensional field values at the false vacua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We reiterate here that in order to solve the differential equation and the bounce action numerically, we have implemented our model in the cosmoTransitions [211] pack- age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The essential parameters that are required for the estimation of GW spectra from FOPT are relative change in energy density during the PT (α), and the inverse of the duration of the PT (β).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Both the parameters, α, and β, are defined at the nucleation temperature Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The first parameter, α, is computed from [216], α = ∆ρ ρrad , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10) where ∆ρ is the released latent heat and it is expressed as [217], ∆ρ = � VT (φ0, T) − T dVT (φ0, T) dT � T=Tn − � VT (φn, T) − T dVT (φn, T) dT � T=Tn , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) – 30 – 340 360 380 400 420 440 460 vN (GeV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 λN tan β = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='77, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='384, κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='012, µ = 203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 GeV, Aλ = 1184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='87 GeV, Aκ = −107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 GeV, AλN = −363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 GeV Allowed by experimental bounds SFOPT along � N direction 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 ∆φ� N/Tn Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This figure shows variations of ∆φ � N/Tn in the vN - λN plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The green-coloured points pass all the experimental constraints as discussed in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The points favoured for SFOPT along the NR field direction are marked by coloured ‘⋆’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed following BP-IV of Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' with φ0 and φn represent, in our case, the four-dimensional field values at the false and true vacua, respectively, and VT (φ, T) is the finite-temperature effective potential as mentioned in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We should note here that the quantity ∆ρ measures the strength of a PT, the larger value of the same corresponds to a stronger FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10), ρrad corresponds to the radiation energy in the plasma and it is expressed as, ρrad = π2g∗ 30 T 4 n, with g∗ being a temperature-dependent quantity that counts the total number of relativistic energy degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The parameter β is defined as [218], β H∗ = T d dT �SE T � ����� T=T∗ ≡ T d dT �SE T � ����� T=Tn , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12) where H∗ is the expansion rate of the Universe during the PT and T∗ stands for the PT temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have considered T∗ ≃ Tn in the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have tabulated the obtained values of α and β in Table 4 for different BPs shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As stated earlier, the quantity α is proportional to the energy released during the PT and hence a larger PT strength should lead to a larger α value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, this is exactly the case where we find the largest α for the BP-III (see Table 4) having ∆φS/Tn = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 (see Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=') We obtain the lowest α for the first-step PT of BP-VI since the corresponding ∆φ � N/Tn is weakest among all as can be seen from Tables 2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 31 – BPs α β/H∗ BP-I 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0456 37535.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 BP-II 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0121 143931.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 BP-III 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0870 11729.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 BP-IV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0101 7596.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 BP-V 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0027 4611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 BP-VI-I 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0002 516911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 BP-VI-II 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0017 63837.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Estimates of the parameters α and β as defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12), respectively for the six BPs listed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that the BP-VI-I shows two-step PT patterns and we have made the estimates of α and β in both steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' There are mainly three different processes that trigger the emission of GWs in a FOPT: (i) bubble wall collisions, (ii) sound waves, and (iii) magneto-hydrodynamic (MHD) tur- bulence in the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Therefore, the total energy spectrum of the emitted GW can approximately be given as a sum of these three contributions [155, 219], ΩGWh2 ≈ Ωcolh2 + Ωswh2 + Ωturh2, respectively, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13) where, h = H0/(100 km · sec−1 · Mpc−1) [220] with H0 corresponding to Hubble’s constant at the present epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The contribution to the total GW energy density from the bubble wall collision can be computed using the envelope approximation and it can be estimated as a function of frequency “f” as [221], Ωcolh2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='67 × 10−5 � β H∗ �−2 � κcα 1 + α �2 �100 g∗ �1/3 � 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11v3 w 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='42 + v2w � 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 (f/fcol)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 1 + 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 (f/fcol)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14) where vw is the bubble wall velocity and κc is the efficiency factor of bubble collision, given as, κc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='715α + 4 27 � 3α 2 1 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='715α .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15) The red-shifted peak frequency fcol [221] is expressed as (with the approximation T∗ ≈ Tn), fcol = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 × 10−6 �f∗ β � � β H∗ � � Tn 100 GeV � � g∗ 100 �1/6 Hz, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16) where the fitting function, f∗/β, at the time of the PT is given by, f∗ β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='62 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1vw + v2w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17) In order to obtain a GW spectrum with higher strength, it is generally assumed that the expanding bubbles attain a relativistic terminal velocity in the plasma and we consider – 32 – vw ≃ 1 in our calculations 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, there is a note of caution that runway bubble walls are generally undesirable in view of the successful yield of a sizeable amount of EWBG 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The contribution to the total GW density from sound waves can be parameterized as [230–233], Ωswh2 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65×10−6 Υ(τsw) � β H∗ �−1 vw � κswα 1 + α �2 � g∗ 100 �1/3 � f fsw �3 � 7 4 + 3 (f/fsw)2 �7/2 , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18) where κsw is the efficiency factor for the sound wave contribution representing the fraction of the energy (latent heat) that gets converted into the bulk motion of the plasma and subsequently emits gravitational waves as given by (in the limit vw → 1) κsw ≃ � α 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='73 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='083√α + α � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19) The quantity fsw corresponds to the present peak frequency for the sound wave contribution to the total GW energy density, expressed as fsw = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 × 10−5 � 1 vw � � β H∗ � � Tn 100 GeV � � g∗ 100 �1/6 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20) The parameter Υ(τsw) appears due to the finite lifetime of the sound waves which suppresses their contributions to the GW energy density as written as Υ(τsw) = 1 − 1 √1 + 2τswH∗ , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='21) with τsw being the lifetime of the sound waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The onset of the turbulence takes place at this timescale and disrupts the sound wave source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Following Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [232], we write τsw ≈ R∗/U f, where R∗ = (8π)1/3 vw/β and U f = � 3κswα/4 are the mean bubble separation and the root-mean-squared fluid velocity which can be obtained from a hydrodynamic analysis, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At the time of PT, the plasma is fully ionized and due to the resulting MHD turbulence, it leads to another source of GWs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The MHD turbulence contribution to the total GW energy density is modelled as [235] Ωturh2 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='35 × 10−4 � β H∗ �−1 vw �κturα 1 + α �3/2 �100 g∗ �1/3 � � (f/ftur)3 [1 + (f/ftur)]11/3 � 1 + 8πf h∗ � � � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22) 14A precise determination of bubble wall velocity is non-trivial [222–226] and out of scope of the present analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Instead, we consider here vw as an input parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 15Recently, an improved analysis on bubble wall dynamics has reported that EWBG may be possible even for supersonic vw [227–229] which is in contrast with our traditional notion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 33 – U-DECIGO U-DECIGO-corr DECIGO-corr BP-I BP-II BP-III 10-7 10-5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='100 10 10-28 10-23 10-18 10-13 10-8 Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Prediction of GW energy density as a function of the frequency for the first three BPs as shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have also highlighted the regions that indicate the proposed sensitivities of the GW experiments namely U-DECIGO and U-DECIGO corr [81, 82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The sensitivity curves for DECIGO and U-DECIGO with correlation analyses are taken from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [234].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' where h∗ = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 × � Tn 100 GeV � � g∗ 100 �1/6 Hz, the inverse Hubble time during GW production, red-shifted to today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The peak frequency ftur is given by, ftur = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7 × 10−5 1 vw � β H∗ � � Tn 100 GeV � � g∗ 100 �1/6 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='23) We set κtur = ϵκsw where ϵ stands for the fraction of the bulk motion which is turbulent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Simulations suggest κtur = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1κsw which we have considered in our numerical calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' U-DECIGO U-DECIGO-corr DECIGO-corr BP-IV BP-V BP-VI-I BP-VI-II 10-7 10-5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='100 10 10-28 10-23 10-18 10-13 10-8 Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Prediction of GW energy density as a function of the frequency for the last three BPs from Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have also highlighted the regions that indicate the proposed sensitivities of the GW experiments namely DECIGO-corr, U-DECIGO and U-DECIGO corr [81, 82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' With these details, in Figure 10 we present the estimates of GW energy density spec- trum as a function of frequency for the first three BPs as shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The predictions – 34 – of ΩGWh2 for the last three BPs of Table 1 are shown in Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We notice from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14), Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22), that each individual contribution to the total GW energy density, ΩGWh2 (as defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13)) is an increasing function of α 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This feature in turn makes ΩGWh2 rise as well for a relatively larger α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In contrast, a larger β H∗ reduces the amount of ΩGWh2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Earlier, in Table 4, we observed that BP-III yields the largest value of α among the six BPs of Table 1 with relatively smaller β H∗ ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Consequently, we find the corresponding peak amplitude of ΩGWh2 to be ∼ O(10−17) for BP-III, which turns out to be the largest as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This feature is depicted in Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The lowest peak am- plitude of ΩGWh2 that we obtain is for the first-step PT of BP-VI which is ∼ O(10−25) as shown in Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The massive suppression to ΩGWh2 for BP-VI-I is caused by the simultaneous presence of a large β H∗ value together with a small α value as shown in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The second-step PT of BP-VI produces a peak having amplitude ∼ O(10−22) which is relatively less suppressed due to a smaller value of β H∗ compared to BP-VI-I as shown in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In view of such estimates, the proposed future GW interferometers namely U-DECIGO and U-DECIGO correlation have the required sensitivities to probe all the BPs, except BP-VI-I, considered in our analysis including BP-I which is preferred in order to address EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We also find it pertinent to mention that the peak frequency of each contribution to GW energy density is linearly proportional to the ratio β H∗ as evident from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is numerically found that the frequency fmax where ΩGWh2 (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13)) attains maximum, also emerges to be an increasing function of β H∗ ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As already noted in Table 4, that BP-VI-I produces the largest β H∗ ratio among all the BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This makes the peak frequency fmax of the corresponding GW spectrum for BP-VI-I the largest among all BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 log10α 2 3 4 5 6 7 log10(β/H∗) SFOPT and possible EWBG SFOPT and no EWBG 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 ∆φSU(2)/Tn −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 log10α 2 3 4 5 6 7 log10(β/H∗) SFOPT and possible EWBG SFOPT and no EWBG 20 40 60 80 100 120 140 160 Tn Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Values of α and β H∗ as a function of ∆φSU(2)/Tn (right) and nucleation temperature Tn (left) for the points in Figure 7 that satisfy the criteria of SFOPT with possible EWBG (depicted by coloured ‘■’) and SFOPT without EWBG (depicted by coloured ‘▲’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 16For α ≫ 1, Ωcolh2, Ωswh2 and Ωturh2 are expected to turn insensitive to the change of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 35 – Earlier in Figure 7 we have identified points in the vN − λN plane that exhibits strong PT along the SU(2)L doublet direction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ∆φSU(2)/Tn > 1, with and without favouring EWBG as highlighted by coloured ‘■’ and ‘▲’ symbols, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Recollect that, in order to prepare Figure 7, we have utilised the fixed values of the other relevant independent parameters as in BP-I, except vN and λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Figure 12, we show the estimates of α and β/H∗, corresponding to the same parameter corner, that is relevant to estimate ΩGWh2 as a function of ∆φSU(2)/Tn (left) and the nucleation temperature Tn (right), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that we are giving particular emphasis on analysing Figure 7 further to compute the GW energy density since it offers the scope of realising EWBG while exhibiting ∆φSU(2)/Tn > 1 (traceable at GW interferometers) at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The Figure 12 illustrates the fact that the points, favoured for EWBG require relatively higher β/H∗ and lower α values compared to the points that do not favour EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This essentially suppresses the peak amplitude of ΩGWh2 for the points favouring EWBG and simultaneously increase the peak frequency fmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The right panel of Figure 12 indicates that a lower Tn tends to increase α which in turn enhance the ∆φSU(2)/Tn leading to larger Ωpeak GW h2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Such features are imprinted in Figure 13 where we have shown the estimates of ΩGWh2 as a function of f for both the coloured ‘■’ and ‘▲’ shaped points, present in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We clearly observe that the points which are not favoured for possible EWBG, produce a larger amount of ΩGWh2 at a particular f and may even fall within the sensitivity curves of LISA [236] and BBO [156].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, the discovery scopes of those points purely depend on the signal-to-noise ratio of the corresponding experiments [237].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 10−5 10−4 10−3 10−2 10−1 100 101 102 103 f [Hz] 10−28 10−25 10−22 10−19 10−16 10−13 10−10 10−7 ΩGWh2(f) LISA BBO DECIGO-corr U-DECIGO U-DECIGO-corr BP-I SFOPT and EWBG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='020 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='030 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='035 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='040 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='045 α 10−5 10−4 10−3 10−2 10−1 100 101 102 103 f [Hz] 10−28 10−25 10−22 10−19 10−16 10−13 10−10 10−7 ΩGWh2(f) LISA BBO DECIGO-corr U-DECIGO U-DECIGO-corr SFOPT and no EWBG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 α Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' GW spectra for the points that show SFOPT in the SU(2)L doublet field directions with (left) and without (right) possible EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that these points are marked by ‘ ■’ and ‘ ▲’ in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For both figures, we keep α as a variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 5 Summary and Conclusion In the present work, we have addressed the properties of EWPT in the RHN superfield extended setup of Z3 invariant NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The RHN extended Z3 invariant NMSSM is cap- tivating due to its ability to provide solutions to the µ−problem of the MSSM and non- – 36 – vanishing neutrino masses and mixing simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In particular, we consider the case where both the LH- and RH-sneutrino receive non-zero VEVs, leading to a spontaneous R- parity-violating scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have worked in an effective field theory set-up by integrating out the heavier squarks, gluinos, as well as sleptons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Additionally, a simple parametriza- tion of the TeV scale seesaw dictates the LH-sneutrino fields to weakly couple to the other relevant fields and thus, is expected to contribute negligibly to the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These facts effectively lead to a four-dimensional field space spanned by the four CP-even Higgses which is of interest in order to explore the PT characteristics in the present framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Without going into the numerical details, one can naively anticipate that in the current setup having a four-dimensional field space, the PT dynamics is likely to be more involved than in the NMSSM where the relevant field space is three-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The EWPT properties and estimate of GW spectrum in the NMSSM have been extensively studied in literature where the roles of NMSSM parameters on the PT strength are also detailed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this work, we scrutinize the role served by the new parameters that appear in theory due to the presence of the RHN superfield on the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In particular, we find that three new parameters λN, AλN and vN leave a non-trivial impact on determining the PT strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the beginning, we describe the model details and successively develop the tools re- quired to study the behaviour of the scalar potential as a function of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We then demonstrate the possible experimental constraints that are of utmost importance to obtain a viable parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Specifically, we undertake constraints arising from the validation of SM Higgs boson properties, BSM Higgs and SUSY searches at colliders, var- ious flavour-violating processes, neutrino experiments and the muon anomalous magnetic moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Since extensive scanning of full parameter space considering a four-dimensional field space, relevant for PT is numerically challenging, we first adopt a benchmark-based analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We provide six BPs that pass through all the experimental constraints and exhibit distinct kinds of FOPT patterns along the different field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have discussed the PT dynamics corresponding to each BP in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' An SFOPT is a prerequisite for EWBG with distinct high-temperature behaviour of the total scalar potential along the SU(2)L field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have shown that BP-I is the preferred BP that exhibits the essential features required for a possible EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, BP-II - BP-V showing SFOPT along the different SU(2)L doublet and singlet field directions in single-step, however, are not suitable for successful EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We find multi-step FOPT for BP-VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' All the BPs listed have one particular feature in common which is the preference for a lighter RH-sneutrino-dominated state below 125 GeV for the occurrence of a FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Next, we utilize a few of the BPs to inquire about the role of new parameters on PT strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Two of the new parameters vN and λN show similar impacts on the PT strength along either of the SU(2)L doublet or singlet field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It turns out that the PT strength increases with the decrease of either vN or λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The remaining parameter AλN has a minor role in the PT along SU(2)L doublet field directions whereas the PT strengths in the SU(2)L singlet field directions get enhanced with the increase of |AλN |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The possible reasons for such unique properties are associated with the impact of the new parameters on the barrier height in the constituent field directions and also the – 37 – lightness of the RH-sneutrino state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, we examine the testability of the BPs by computing the GW energy density corresponding to each BP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have considered all possible sources that trigger GW emis- sion in a FOPT namely, bubble wall collisions, sound waves and magneto-hydrodynamic turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The highest peak amplitude of the GW energy density that we obtain is for BP-III which lies within the proposed sensitivity of DECIGO correlation data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The peak amplitude of ΩGWh2 for other BPs is relatively weaker, however, within the reach of U- DECIGO and U-DECIGO-corr sensitivities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is to be noted that a TeV scale canonical seesaw model with RHN weakly coupled to SM particles is extremely difficult to probe at collider experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Our analysis infers an alternative albeit promising pathway to validate a TeV scale seesaw model at future GW interferometers beyond colliders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the present work, we have not performed an exact prediction of the baryon asym- metry of the Universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Instead, we find the corner of the parameter space that shows SFOPT along the SU(2)L doublet field directions and facilitates EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Improvement of our analysis is possible by precise computation of bubble wall profile, bubble wall velocity, and CP-violation that decide the final amount of baryon asymmetry of the Universe, which is also correlated with NMSSM + RHN model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In an R-parity violating theory like the present one, gravitino can be a potential decaying dark matter candidate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Future works may also include investigating the correspondence between gravitino dark matter phenomenology and NMSSM + RHN parameter space, favouring an SFOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Acknowledgements P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' acknowledges the financial support received from the Indian Institute of Technology, Delhi (IITD) as a Senior Research Fellow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' acknowledges the IITD SEED grant sup- port IITD/Plg/budget/2018-2019/21924, continued as IITD/Plg/budget/2019- 2020/173965, IITD Equipment Matching Grant IITD/IRD/MI02120/208794, and Start-up Research Grant (SRG) support SRG/2019/000064 from the Science and Engi- neering Research Board (SERB), Department of Science and Technology, Government of India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' is supported by NPDF grant PDF/2020/000797 from the SERB, Govern- ment of India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' also acknowledge Mikael Chala, Bo-Qiang Lu, Jiang Zhu and Kaius Loos for useful communications regarding cosmoTransitions code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A Field dependent mass matrices Our numerical studies are based on the field-dependent masses (see subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The corresponding scalar squared mass terms are evaluated at T = 0 using the tree-level un- coloured scalar potential Vscalar (see below), including only the dominant higher-order con- tributions ∆V (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mathematically, for the uncoloured scalar squared mass matrices M2 X,ij = M2 φαφβ(HSM, HNSM, HS, NR) ≡ ∂2Vscalar ∂φα∂φβ ���� φα̸=0 , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where X = S (for the CP-even neutral scalar) or A (for the CP-odd neutral scalar) and i, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, φα(β) = HSM, HNSM, HS, NR, ℜ(�ν1,2,3) for the CP-even neutral – 38 – scalar and φα(β) = ANSM, AS, G0, NI, ℑ(�ν1,2,3) for the CP-even neutral scalar, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For the uncoloured electrically charged scalar, X = C with i, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', 8 and φα(β) ≡ C+ = H+, G+, �e+ L, �µ+ L, �τ + L , �e+ R, �µ+ R, �τ + R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here, we have used �νi = ℜ�νi + iℑ�νi √ 2 ≡ νRi + i�νIi √ 2 with i = 1, 2, 3 ≡ e, µ, τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) The full uncoloured scalar potential is given by Vscalar = ����� 3 � i=1 Y i N �νi � N − λSH0 d ����� 2 + ������ 3 � i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='j=1 Y ij e �li�ec j − λSH0 u ������ 2 + ������ Y i NH0 u � N − 3 � j=1 Y ij e H− d �ec j ������ 2 + ����λHu · Hd + κS2 + λN 2 � N 2 ���� 2 + ����� 3 � i=1 Y i N �Li · Hu + λNS � N ����� 2 + ����� 3 � i=1 Y ij e Hd · �Li ����� 2 + ������ λSH+ u − 3 � i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='j=1 Y ij e �νi�ec j ������ 2 + �����λSH− d − 3 � i=1 Y i N�li � N ����� 2 + ������ 3 � j=1 Y ij e H0 d�ec j − Y i NH+ u � N ������ 2 + g2 1 8 (|Hd|2 − |Hu|2 + |�Li|2 − 2|�ec i|2)2 + g2 2 2 3 � a=1 � H† d τ a 2 Hd + H† u τ a 2 Hu + �L† i τ a 2 �Li �2 + m2 Hd|Hd|2 + m2 Hu|Hu|2 + m2 S|S|2 + M 2 N| � N|2 + 3 � i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='j=1 m2 �Lij �Lm∗ i �Lm j + 3 � i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='j=1 m2 �ec ij�ecm∗ i �ecm j + 3 � i=1 (AeYe)ijHd · �Li�ec j + λAλSHu · Hd + (ANYN)i�Li · Hu � N + κAκ 3 S3 + λNAλN 2 S � N 2 + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) Here Y ij e belongs to W ′ MSSM (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1)) and m2 Hd, m2 Hu, m2 �Lij, m2 �ec ij, (AeYe)ij are encapsulated within −L′ soft (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, i, j are generation indices, τ as are Pauli spin matrices and m = 1, 2, as per the standard notation (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [27, 83–85, 87, 88] for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In a similar way, one can derive field-dependent mass matrices for the uncoloured elec- trically neutral and electrically charged fermions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', neutralinos and charginos, directly from the superpotential W (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mathematically, the generic mass term for the neutralino sector and the chargino sector are given by − 1 2 � ψ0T i M0ijψ0 j + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' � , −1 2(ψ+, ψ−)T Mχ±(ψ+, ψ−) + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here basis for the neutralino sector is given by ψ0T = { �B0, � W 0 3 , �H0 d, �H0 u, �S, N, ν1, ν2, ν3} involving neutral U(1)Y , SU(2)L gauginos ( �B0, � W 0 3 ), neutral higgsinos ( �H0 d, �H0 u), singlino (�S), RH-neutrino (N) and LH-neutrinos (ν1,2,3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For charginos, including charged SU(2)L gauginos (� W ±), charged higgsinos ( �H+ u , �H− d ) and charged leptons (e± L, R, µ± L, R, τ ± L, R), one gets ψ+T = {� W +, �H+ u , e+ R, µ+ R, τ + R } and ψ−T = {� W −, �H− d , e− L, µ− L, τ − L }, respec- – 39 – tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We will start with the scalar mass squared matrices and will discuss the fermionic sector subsequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 CP-even neutral scalars squared mass matrix In the basis HSM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' HNSM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' HS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' NR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' ℜ(�ν1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' non-zero entries of the symmetric M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='ij are M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 ≃ 1 16vuvd � 8λvSv2 (Aλ + κvS) + 2λ2vuvd � −4 � v2 + 2v2 S � + H2 NSM + 4H2 S + 3H2 SM � +vuvd � 3∆λ2 + G2� � H2 NSM + 3H2 SM � −4 cos 2β � v2 cos 2β � 2λvS (Aλ + κvS) + vuvd � G − 2λ2� vu � + 3∆λ2vuvdH2 SM � +vuvd � (4 sin 2β � 3∆λ2HNSMHSM − 2λHS �√ 2Aλ + κHS �� −3 � ∆λ2 + G − 2λ2� � 2 sin 4β HNSMHSM + cos 4β � H2 NSM − H2 SM �� �� − 1 2v �λNv 2 sin 2β � N2 R − 2v2 N �� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) M2 S,12 ≃ 1 16vuvd �2v2 sin 4β � 2λvS (Aλ + κvS) + vuvd � G − 2λ2�� vuvd −8λ cos 2β HS �√ 2Aλ + κHS � + 3 sin 4β � ∆λ2 + G − 2λ2� � H2 NSM − H2 SM � −6 cos 4β HNSMHSM � ∆λ2 + G − 2λ2� + 2HNSMHSM � 3∆λ2 + G + 2λ2� +6∆λ2 sin 2β � H2 NSM + H2 SM � � − 1 4 � λ cos 2β λN � N2 R − 2v2 N � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) M2 S,13 ≃ λ2HSHSM − 1 2λ �√ 2Aλ + 2κHS � (cos 2β HNSM + sin 2β HSM) , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) M2 S,14 ≃ −1 2λλNNR (cos 2β HNSM + sin 2β HSM), (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8) M2 S,1 (4+i) ≃ 1 2NRY i N �√ 2AN sin β + HS (λ cos β + λN sin β) � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) M2 S,22 ≃ 1 16vuvd � 8λvSv2 (Aλ + κvS) + vuvd (3∆λ2 + G) � 3H2 NSM + H2 SM � +2λ2vuvd � −4 � v2 + 2v2 S � + 3H2 NSM + 4H2 S + H2 SM � +4 cos 2β � v2 cos 2β � 2λvS (Aλ + κvS) + vdvu � G − 2λ2�� + 3∆λ2vdH2 NSMvu � +vdvu � 4 sin 2β � 2λHS �√ 2Aλ + κHS � + 3∆λ2HNSMHSM � +3 � ∆λ2 + G − 2λ2� � 2 sin 4β HNSMHSM + cos 4β � H2 NSM − H2 SM �� �� + 1 8v � cos β cot βλN � λv(cos 4β + 3) sec3 βv2 N + 4λv sin β tan β N2 R �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10) 17While writing field-dependent masses, we ignore terms that are quadratic in vi, Y i N and terms like 3� i=1 viY i N, keeping in mind their smallness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, as already stated, these terms do not play any crucial role in the EWPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, we have kept all these terms in our numerical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 40 – M2 S,23 ≃ 1 2λ �√ 2Aλ + 2κHS � (sin 2β HNSM − cos 2β HSM) + λ2HNSMHS,(A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) M2 S,24 ≃ 1 2λλNNR (sin 2β HNSM − cos 2β HSM), (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12) M2 S,2 (4+i) ≃ 1 2NRY i N �√ 2AN cos β + HS (cos β λN − λ sin β ) � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13) M2 S,33 ≃ λvuvd (Aλ + 2κvS) vS + κ � Aκ �√ 2HS − vS � + κ � 3H2 S − 2v2 S �� − λ2v2 +λ2 2 � H2 NSM + H2 SM � − λκ cos 2β HNSMHSM + λκ 2 sin 2β � H2 NSM − H2 SM � + 1 2vS � λN � (κ + λN) vS � N2 R − 2v2 N � − v2 NAλN �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14) M2 S,34 ≃ 1 2λNNR ���√ 2AλN + 2 (κ + λN) HS � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15) M2 S,3 (4+i) ≃ 1 2Y i NNR (HNSM (λN cos βλ sin β ) + HSM (λ cos β + λN sin β )), (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16) M2 S,44 ≃ 1 4vN � − 2λλN cos 2β HNSMHSMvN+λ sin 2β vNλN � H2 NSM − H2 SM + 2v2� +λNvN � 2AλN �√ 2HS − 2vS � + 2 (κ + λN) H2 S � +λNvN � λN � 3N2 R − 2v2 N � − 4 (κ + λN) v2 S � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17) M2 S,4 (4+i) ≃ 1 2Y i N �√ 2AN (cos β HNSM + sin β HSM) + HS � HNSM (λN cos β − λ sin β) +HSM (λ cos β + λN sin β) �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18) M2 S,(4+i) (4+j) ≃ δij 8 � − 2G sin 2β HNSMHSM − G cos 2β � H2 NSM − H2 SM � −8vNY i N (vu (AN + λNvS) + λvdvS) vi − 2Gv2 cos 2β � −1 4g2 2 (sin β HNSM − cos β HSM) 2, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19) where we have used G = g2 1 + g2 2, v2 u + v2 d = v2 and i = 1, 2, 3 are generational indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 CP-odd neutral scalars squared mass matrix In the basis ANSM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' AS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' G0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' NI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' ℑ(�ν1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' non-zero entries of the symmetric M2 A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='ij are M2 A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 ≃ 1 16vdvu � 8λvSv2 (Aλ + κvS) + Gvdvu � H2 NSM − H2 SM � +2λ2vdvu � −4 � v2 + 2v2 S � + H2 NSM + 4H2 S + 3H2 SM � + ∆λ2vdvu � 3H2 NSM + H2 SM � +4 cos 2β � v2 cos 2β � 2λvS (Aλ + κvS) + vuvd � G − 2λ2�� + ∆λ2vuvdH2 NSM � +vuvd � 4 sin 2β � 2λHS �√ 2Aλ + κHS � + ∆λ2HNSMHSM � + � ∆λ2 + G − 2λ2� � 2 sin 4β HNSMHSM + cos 4β � H2 NSM − H2 SM �� �� + 1 8v � cos β cot β λN � λv(cos 4β + 3) sec3 β v2 N + 4λv sin β tan β N2 R �� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20) – 41 – M2 A,12 ≃ 1 2λHSM �√ 2Aλ − 2κHS � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='21) M2 A,13 ≃ 1 16 �2v2 sin 4β � 2λvS (Aλ + κvS) + � G − 2λ2� vuvd � vuvd −8λ cos 2β HS �√ 2Aλ + κHS � + 2∆λ2 sin 2β � H2 NSM + H2 SM � +2HNSMHSM � ∆λ2 + G − 2λ2� − 2 cos 4β HNSMHSM � ∆λ2 + G − 2λ2� + sin 4β � ∆λ2 + G − 2λ2� (HNSM − HSM) (HNSM + HSM) � − 1 4v � λλNv cos 2β � N2 R − 2v2 N � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22) M2 A,14 ≃ −1 2λλNHSMNR, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='23) M2 A,1 (4+i) ≃ −1 2Y i NNR �√ 2AN cos β + HS (cos β λN ��� λ sin β ) � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24) M2 A,22 ≃ λvuvd (Aλ + 2κvS) vS − κAκ �√ 2HS + vS � − 1 2λ2 � 2v2 + H2 NSM + H2 SM � +λκ cos 2β HNSMHSM + λκ sin β cos β � H2 SM − H2 NSM � + κ2 � H2 S − 2v2 S � − 1 2vS � λN � (v2 NAλN + vS � 2v2 N (κ + λN) + N2 R (κ − λN) � �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='25) M2 A,23 ≃ −1 2λHNSM �√ 2Aλ − 2κHS � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='26) M2 A,24 = −1 2λNNR �√ 2AλN − 2κHS � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='27) M2 A,2 (4+i) ≃ Y i N 2 NR (HNSM (λN cos β − λ sin β) + HSM (λ cos β + λN sin β)), (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='28) M2 A,33 ≃ 1 16vuvd � 8λvSv2 (Aλ + κvS) − Gvuvd � H2 NSM − H2 SM � +2λ2vuvd � −4 � v2 + 2v2 S � + 3H2 NSM + 4H2 S + H2 SM � + ∆λ2vuvd � H2 NSM + 3H2 SM � −4 cos 2β � v2 cos 2β � 2λvS (Aλ + κvS) + vuvd � G − 2λ2�� + ∆λ2vdH2 SMvu � +vuvd � 4 sin 2β � ∆λ2HNSMHSM − 2λHS �√ 2Aλ + κHS �� − � ∆λ2 + G − 2λ2� � 2 sin 4β HNSMHSM + cos 4β � H2 NSM − H2 SM �� �� − 1 2v � λλNv sin β cos β � N2 R − 2v2 N �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='29) M2 A,34 ≃ 1 2λλNHNSMNR, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='30) M2 A,3 (4+i) ≃ −Y i N 2 NR �√ 2AN sin β + HS (λ cos β + sin β λN) � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='31) – 42 – M2 A,44 ≃ 1 4vN � 2λλN cos 2βHNSMHSMvN +λλN sin 2βvN � −H2 NSM + H2 SM + 2v2� +λNvN � − 2AλN �√ 2HS + 2vS � + 2 (λN − κ) H2 S � +λNvN � λN � N2 R − 2v2 N � − 4v2 S (κ + λN) �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='32) M2 A,4 (4+i) ≃ Y i N 2 � HS � HNSM (λ sin β + λN cos β) + HSM (λN sin β − λ cos β) � − √ 2AN (cos βHNSM + sin β HSM) � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='33) M2 A, (4+i)(4+j) ≃ − δij 8vj � G cos 2βvj � H2 NSM − H2 SM + 2v2� + 2Gvj sin 2β HNSMHSM +8v sin β vNY j N (AN + λNvS) + 8λv cos β vNY j NvS � −1 4g2 2 (sin β HNSM − cos β HSM)2, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='34) M2 A, 56 ≃ Y 1 NY 2 N 2 (cos βHNSM + sin βHSM)2 , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='35) M2 A, 57 ≃ Y 1 NY 3 N 2 (cos βHNSM + sin βHSM)2 (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='36) M2 A,67 ≃ Y 2 NY 3 N 2 (cos β HNSM + sin β HSM)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='37) where we have used G = g2 1+g2 2, v2 u+v2 d = v2 and i = 1, 2, 3 are generational indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At the physical vacuum, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', � ⟨HSM⟩, ⟨HNSM⟩, ⟨HS⟩, ⟨NR⟩ � = �√ 2v, 0, √ 2vS, √ 2vN � , neglecting terms like v2 i , Y i2 N , 3� i=1 viY i N, the Goldstone mode appears massless and decouples from the other CP-odd states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Uncoloured charged scalars squared mass matrix Non-zero entries for the uncoloured symmetric charged scalar mass squared matrix, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=',' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C+MCC−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' in the basis C+ = H+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' G+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �e+ L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �µ+ L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �τ + L ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �e+ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �µ+ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �τ + R are M2 C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 ≃ 1 16 � 2 cos 2βg2 1 � 2 sin 2βHNSMHSM + cos 2β(2v2 + H2 NSM − H2 SM) � +g2 2 � (1 + cos 4β)H2 NSM + 2 sin 4βHNSMHSM − (−3 + cos 4β)H2 SM + 2v2(1 + cos 4β) +4 cos 2β � − 4v2λ2(3 + cos 4β) + 2λ2(4H2 S + (−1 + cos 4β)H2 SM) − 16λ2v2 s +2∆λ2 sin2 2βH2 SM +4(λ2 sin2 2β + ∆λ22 cos4 β)H2 SM + 4(λ2 sin 4β − 4∆λ2 cos3 β sin β)HNSMHSM +4λvSAλ(3 + cos 4β) csc β sec β + 4λ sin β � 2HS( √ 2Aλ + κHS + λNN2 R) � +4λ(3 + cos 4β) csc 2β(2κv2 S + v2 NλN) � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='38) – 43 – M2 C,12 ≃ 1 16 � � 2 cos 4β(2λ2 − G − ∆λ2) + 2(2λ2 + g2 1 − g2 2 + ∆λ2) � HNSMHSM +2 sin 2β∆λ2(H2 NSM + (1 + 2 sin2 β)H2 SM) + sin 4β � (G − 2λ2)(2v2 + H2 NSM − H2 SM) + (H2 NSM − H2 SM)∆λ2 � +8λ cos 2β � κH2 S + Aλ( √ 2HS − 2vS) − 2κv2 S + λN 2 (N2 R − 2v2 N) � � ,(A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='39) M2 C1, (2+i) ≃ δij 4 � vj � � g2 2 cos 2β + 2(Y ij e )2 sin2 β � HNSM + sin 2β � g2 2 − (Y ij e )2� HSM � −2Y j NNR �√ 2AN cos β + cos β � λNHS − Y ij e (sin βHNSM − cos βHSM) � + λ sin βHS �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='40) M2 C,1 (5+i) ≃ − 1 √ 2AeY ij e vj sin β − 1 2Y ij e Y j N sin β(NR) (cos βHNSM + sin βHSM) , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='41) M2 C,22 ≃ 1 16 � 2G cos2 β(H2 SM − 2v2) + 4λ2 sin2 2β(H2 SM − 2v2) + 8λ2(H2 S − 2v2 S) + � − 2g2 1 cos2 2β + g2 2(cos 4β − 3) + (cos 4β − 1)(2λ2 − ∆λ2) � H2 NSM +2 � sin 4β(2λ2 − G)8 cos β sin3 β∆λ2 � HSMHNSM + 4λ sin 2β � − 2κH2 S +4κv2 S + Aλ � −2 √ 2HS + 4vS − λN(N2 R − 2v2 N) � �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='42) M2 C2, (2+i) ≃ δij 4 � vj � � −g2 2 cos 2β − 2(Y ij e )2 sin2 β � HSM + sin 2β � g2 2 − (Y ij e )2� HNSM � −2Y j NNR �√ 2AN sin β + sin β � λNHS − Y ij e (sin βHNSM − cos βHSM) � − λ cos βHS �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='43) M2 C,2 (5+i) ≃ −(AeYe)ij √ 2 vj cos β − 1 2Y ij e Y j NNR � cos2 βHNSM + sin 2β 2 HSM �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='44) M2 C,(2+i)(2+j) ≃ m2 �Lij + δij 8 � (g2 1 − g2 2)(cos 2β(H2 SM − H2 NSM) − 2 sin 2βHSMHNSM) +4(Y ij e )2(cos βHSM − sin βHNSM)2 � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='45) M2 C,(2+i)(5+j) ≃ δij(AeYe)ij √ 2 (cos βHSM − sin βHNSM) −δijλY ij e 2 (cos βHNSM + sin βHSM)HS, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='46) M2 C,(5+i)(5+j) ≃ m2 �ec ij − δij 4 � g2 1(cos 2β(H2 SM − H2 NSM) − 2 sin 2βHSMHNSM) −2(Y ij e )2(cos βHSM − sin βHNSM)2 � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='47) – 44 – where we have used G = g2 1+g2 2, v2 u+v2 d = v2 and i = 1, 2, 3 are generational indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At the physical vacuum, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', � ⟨HSM⟩, ⟨HNSM⟩, ⟨HS⟩, ⟨NR⟩ � = �√ 2v, 0, √ 2vS, √ 2vN � , neglecting terms like v2 i , Y i2 N , 3� i=1 viY i N, the Goldstone mode appears massless and decouples from the other charged states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 Neutralino mass matrix In the basis of ψ0T = { �B0, � W 0 3 , �H0 d, �H0 u, �S, N, ν1, ν2, ν3}, the matrix M0 (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4)) is given as M0 = � � � M6×6 m6×3 mT 3×6 03×3 � � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='48) where we have used ⟨�νi⟩ = vi (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6)) as the LH-sneutrinos are not dynamical in nature (see subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, matrices mT 3×6 and M6×6, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8), are given as mT 3×6 = � � � � � � � � � −g1ve √ 2 g2ve √ 2 0 Y 1 NNR √ 2 0 Y 1 N √ 2Y −g1vµ √ 2 g2vµ √ 2 0 Y 2 NNR √ 2 0 Y 2 N √ 2Y −g1vτ √ 2 g2vτ √ 2 0 Y 3 NNR √ 2 0 Y 3 N √ 2Y � � � � � � � � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='49) with Y = � sβHSM + cβHNSM � and the symmetric matrix M6×6 is given as, � � � � � � � � � � � � � � � � � � � � � � M1 0 − g1 2 X g1 2 Y 0 0 M2 g2 2 X − g2 2 Y 0 0 0 − λ √ 2HS − λ √ 2Y 0 0 − λ √ 2X 0 √ 2κHS λN 2 √ 2NR λN √ 2HS � � � � � � � � � � � � � � � � � � � � � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='50) where we have omitted symmetric entries, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', M0ij = M0ji for ̸= j and X = � cβHSM − sβHNSM � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 Chargino mass matrix Using a similar approach, in the basis ψ+T = {� W +, �H+ u , e+ R, µ+ R, τ + R } and ψ−T = {� W −, �H− d , e− L, µ− L, τ − L }, the matrix M± is given as M± = � 0 XT X 0 � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='51) – 45 – where the 5 × 5 matrix X is given by � � � � � � � � � � � � � � � � � � M2 g2 √ 2Y 0 0 0 g2 √ 2X λ √ 2HS −Y 11 e ve −Y 22 e ve −Y 33 e vτ g2ve − Y 1 N NR √ 2 Y 11 e √ 2 X 0 0 g2vµ − Y 2 N NR √ 2 0 Y 22 e √ 2 X 0 g2vτ − Y 3 N NR √ 2 0 0 Y 33 e √ 2 X � � � � � � � � � � � � � � � � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='52) Here we have used Y ij e = Y ii e δij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B Neutral scalar mass matrices after the EWSB Weak couplings among the LH-handed sneutrino states and the remaining states, as already discussed in section 2, suggest that one can safely decouple the LH-sneutrino-dominated states from the CP-even and CP-odd scalar squared mass matrices without any loss of generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' After the aforesaid detachment, both CP-even and CP-odd scalar squared mass matrices appear to be 4 × 4 in size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The full 7 × 7 squared mass matrices are given in subsections A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 & A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, including LH-sneutrino states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this section, squared mass matrices of the CP-even and the CP-odd Higgses are given after the EW symmetry breaking, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', using relations given in subsections A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 & A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 and considering ⟨HSM⟩ = √ 2v, ⟨HNSM⟩ = 0, ⟨HS⟩ = √ 2vS, ⟨NR⟩ = √ 2vN, ⟨ANSM⟩ = 0, ⟨AS⟩ = 0, ⟨NI⟩ = 0 (see subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For the CP-even states, we consider the {HSM, HNSM, HS, NR} basis while for the CP-odd ones we use {ANSM, AS, G0, AN} basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 CP-even mass squared elements M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 = λ2v2 sin2 2β + (g2 1 + g2 2)v2 2 cos2 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 = λ2v2 2 sin 4β − (g2 1 + g2 2)v2 4 sin 4β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13 = 2λ2vvS − λv(Aλ + 2κvS) sin 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 = −λλNvN sin 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22 = 2λvS(Aλ + κvS) csc 2β + λλNv2 N csc 2β − λ2v2 sin2 2β + (g2 1 + g2 2)v2 2 sin2 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='23 = −λv(Aλ + 2κvS) cos 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 = −λλNvvN cos 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='33 = κvS(Aκ + 4κvS) + λv2Aλ 2vS sin 2β − λNv2 NAλN 2vS ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='34 = λNvNAλN + 2λNκvSvN + 2λ2 NvSvN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='44 = λ2 Nv2 N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where we have used the symmetric nature of these entries, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', M2 S,ij = M2 S,ji for i ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 46 – B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 CP-odd mass squared elements M2 A,11 = λλNv2 N csc 2β + 2λvS(Aλ + κvS) csc 2β, M2 A,12 = λvAλ − 2λκvvS, M2 A,13 = 0, M2 A,14 = −λλNvvN, M2 A,22 = κ(2λv2 sin 2β − 3vSAκ) + λv2Aλ 2vS sin 2β − λNv2 N 2vS (AλN + 4κvS), M2 A,23 = 0, M2 A,24 = 2λNκvSvN − λNvNAλN , M2 A,33 = 0, M2 A,34 = 0, M2 A,44 = λλNv2 sin 2β − 2λNvS(AλN + κvS), (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) where we have used the symmetric nature of these entries, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', M2 A,ij = M2 A,ji for i ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C Counter terms As already addressed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, after including Coleman-Weinberg contributions (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15)), counter terms are necessary to restore the original physical minima and masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These terms are encapsulated within Vct which is written as Vct = δm2 Hd |Hd|2 + δm2 Hu |Hu|2 + δm2 S |S|2 + δM2 N | � N|2 + δλAλ (SHu · Hd + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=') +δλNAλN (S � N � N + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=') + δλ2 2 |Hu|4, (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where δm2 Hd, δm2 Hu, δm2 S, δM2 N , δλAλ, δλNAλN , δλ2 are counter terms corresponding to en- tries given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Entries corresponding to δm2 Hd, δm2 Hu are encapsu- lated within −L′ soft of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In order to maintain the location of the physical minima solutions for the counter-terms must satisfy the following relations: δm2 Hd = 1 √ 2v � tan β ∂Veff ∂HNSM − ∂Veff ∂HSM � + µ sec2 β 2λv ∂2Veff ∂HS∂HSM ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δm2 Hu = csc2 β 4vλ ∂ ∂HSM �√ 2λ(cos 2β − 2) Veff + 2µ∂Veff ∂HS + 2λv ∂Veff ∂HSM � − 1 √ 2v cot β ∂Veff ∂HNSM ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δm2 S = λ 2µ ∂ ∂HS � v ∂Veff ∂HSM + vN ∂Veff ∂NR − √ 2 Veff � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δM2 N = − 1 2vN ∂ ∂NR �√ 2 Veff − 2µ λ ∂Veff ∂HS � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δλAλ = csc 2β v ∂2Veff ∂HS∂HSM ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δλNAλN = − 1 2vN ∂2Veff ∂HS∂NR ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δλ2 = csc4 β 4v3 ∂ ∂HSM �√ 2 Veff − 2v ∂Veff ∂HSM � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) – 47 – Identifying δλ2 as a counter term for ∆λ2, a quartic coupling among Hu as given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12), seems inconsistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, in reality, ∆λ2 is connected to the soft SUSY-breaking terms as the estimation of ∆λ2 includes soft SUSY-breaking terms of the stop sector (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D Daisy coefficients The Daisy coefficients [133–137], ci, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18) is given by ci = m2 i (φα, T) − m2 i (φα) T , (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) and can be estimated using the high-temperature limit, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', T 2 ≫ m2 (m depicts a generic mass term involved in the calculation) [133], of the thermal corrections from V T̸=0 1−loop (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17)) as 1 T 2 ∂2V 1−loop T̸=0 ∂φi∂φj .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) Daisy coefficients are calculated at the T 2 ≫ m2 limit which helps to efface gauge depen- dence for these coefficients although V 1−loop T̸=0 , as already discussed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3, has explicit gauge dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The form of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2), except the 1/T 2 factor, looks similar to relations that are conventionally used for the computation of i, j-th entry of the different scalar mass matrices from the concerned potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For the calculation of Daisy coefficients we use V 1−loop T̸=0 as a function of m2 i (φα) and not as a function of m2 i (φα, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, while computing V 1−loop T̸=0 and V ′1−loop CW (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20)) we use thermal masses m2 i (φα, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Expanding thermal function JB/F (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19)), in the limit T 2 ≫ m2, one gets in the leading order [137, 238] V T̸=0 1−loop ∼ T 2 48 � 2 � i=B nim2 i + � i=F nim2 i � , (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) where B(F) represents boson (fermion) and ni depicts the associated degrees of freedom, as already detailed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is also apparent from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) that contribu- tions from the bosonic sources are the leading ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Also, as detailed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [137], cubic contributions in the V T̸=0 1−loop appears only via bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, quartic contributions from fermions are suppressed compared to the same from bosons and do not affect the shift in the VEVs [137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, we neglect contributions from the relevant fermionic sources (see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [239] for a similar discussion in the context of the NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In light of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3), non-zero Daisy coefficients are given below where field-dependent masses – 48 – are considered as a function of all bosonic degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cHSMHSM = cG0G0 = λ2 4 + (3m2 Z + 4m2 W ) 8v2 + m2 Z 4v2 sin2 θw cos2 β + m2 t 4v2 + ∆λ2 4v2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cHSMHNSM = cHNSMG0 = m2 t 4v2 1 tan2 β + ∆λ2 sin 2β 8 − m2 Z 8v2 sin2 θw sin 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cHNSMHNSM = cANSMANSM = λ2 4 + (m2 Z + 4m2 W ) 8v2 + m2 t 4v2 tan2 β + m2 Z 4v2 sin2 θw sin2 β + ∆λ2 4 cos2 β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cHSHS = λ2 + κ2 2 + λ2 N 8 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cASAS = λ2 + κ2 3 + λ2 N 12 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cNRNR = λ2 N 4 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cNINI = λ2 N 6 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cH+H− = λ2 6 + (m2 Z + 8m2 W ) 24v2 − m2 Z 4v2 sin2 θw sin2 β + m2 t 4v2 tan2 β 1 tan2 β + ∆λ2 4 cos2 β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cH+G− = m2 t 4v2 tan2 β 1 tan2β + ∆λ2 sin 2β 8 − m2 Z 8v2 sin2 θw sin 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cG+G− = λ2 6 + (7m2 Z + 8m2 W ) 24v2 − m2 Z 4v2 sin2 θw sin2 β + m2 t 4v2 + ∆λ2 4 sin2 β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) where mW , mZ represent masses for the W ±, Z0 bosons, respectively and θw is Weinberg angle [110].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Longitudinal modes of the massive gauge bosons also yield non-zero Daisy coefficients [240, 241] cW + L W − L = cW 3 LW 3 L = 5 2g2 2, cBLBL = 13 6 g2 1, (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) where W ± L , W 3 L, BL correspond to longitudinal modes of the SM SU(2)L, U(1)Y gauge bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These results are the same as the Z3-invariant NMSSM as gauge sector of the chosen NMSSM + one RH-neutrino framework remains exactly the same as the Z3-invariant NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, at T ̸= 0 the photon (γ) also gets a temperature-dependent mass, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', a non-vanishing longitudinal component, which should also be included in the field-dependent mass matrix used to evaluate eigenvalues of the electrically neutral EW gauge bosons, γ, Z0 at T ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' m2 ZLγL(HSM, HNSM, HS, NR, T) = � � � g2 2 H2 SM+H2 NSM 4 + 5 2g2 2T 2 −g1g2 H2 SM+H2 NSM 4 −g1g2 H2 SM+H2 NSM 4 g2 1 H2 SM+H2 NSM 4 + 13 6 g2 1T 2 � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) E Minimization conditions As already stated in section 3 that one can trade different soft-masses, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', m2 Hu, m2 Hd, m2 �Lij, m2 S, M2 N (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2)) with the corresponding VEVs (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6)) using min- imization conditions of the Vtree (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can also use the neutral part of Vscalar as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mathematically, the minimization condition gives a set of – 49 – equations like �∂Vtree ∂Xi ����� X=⟨X⟩ = 0, (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where Xi = H0 u, H0 d, �νi, S, � N, and ⟨X⟩ represents all the concerned VEVs as given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In detail, assuming all superpotential couplings (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1)) to be real, one gets �∂Vtree ∂H0u ����� VEVs = λvd � λvuvd − κv2 S − λN 2 v2 N � + Y i2 N v2 Nvu + λ2v2 Svu + m2 Huvu + 3 � j=1 Y j Nvj � 3 � i=1 Y i Nvivu + λNvSvN � + g2 1 + g2 2 4 � v2 d + 3 � i=1 v2 i − v2 u � vu + λAλvSvd + 3 � i=1 (ANYN)ivivN, (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) �∂Vtree ∂H0 d ����� VEVs = λvu � λvuvd − κv2 S − λN 2 v2 N � + λvS � λvSvd − 3 � i=1 Y i NvivN � + g2 1 + g2 2 4 � v2 d + 3 � i=1 v2 i − v2 u � vd + m2 Hdvd + λAλvSvu, (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) �∂Vtree ∂ �νi ����� VEVs = Y i Nvu � � 3 � j=1 Y j Nvjvu + λNvSvN � � + Y i NvN � � 3 � j=1 Y j NvjvN − λvdvS � � + g2 1 + g2 2 4 � v2 d + 3 � i=1 v2 i − v2 u � vi + (ANYN)ivuvN + 3 � j=1 m2 �Lijvj, (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) �∂Vtree ∂S ����� VEVs = 2κvS � −λvuvd + κv2 S + λN 2 v2 N � + λvd � λvSvd − 3 � i Y i NvivN � + λNvN � 3 � i=1 Y i Nvivu + λNvSvN � + λ2v2 uvS + m2 SvS + λAλvuvd + κAκv2 S + λNAλN 2 v2 N, (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) �∂Vtree ∂ � N ����� VEVs = λNvN � −λvuvd + κv2 S + λN 2 v2 N � + λNvS � 3 � i=1 Y i Nvivu + λNvSvN � + 3 � j=1 Y j Nvj � 3 � i=1 Y i NvivN − λvSvd � + Y i2 N v2 uvN + M2 NvN + 3 � i=1 (ANYN)ivivu + λAλN vSvN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) – 50 – References [1] Planck collaboration, Planck 2018 results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 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