diff --git "a/-9E5T4oBgHgl3EQfRw7N/content/tmp_files/load_file.txt" "b/-9E5T4oBgHgl3EQfRw7N/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/-9E5T4oBgHgl3EQfRw7N/content/tmp_files/load_file.txt" @@ -0,0 +1,735 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf,len=734 +page_content='Veltman Criteria in Beyond Standard Model Effective Field Theory of Complex Scalar Triplet aJaydeb Das 1, bNilanjana Kumar2 a Department of Physics and Astrophysics, University of Delhi, Delhi-110007, India bCentre For Cosmology and Science Popularization (CCSP), SGT University, Gurugram, Haryana-122006, India Abstract The Standard Model Higgs mass, not being protected by any symmetry, suffers from large correction terms due to quadratic divergence coming from the self energy corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Veltman Condition (V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=') ensures that the coefficient of the quadratic divergent term either vanishes or becomes negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' If the Standard Model (SM) is valid upto a scale (Λ) and new physics exists after that, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' demands Λ ≲ 760 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' But the non-observation of new physics has pushed the scale to be ≥ 1 TeV already, making it impossible to satisfy V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' in the Standard Model without very large fine tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Attempts has been made to satisfy the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' in many Beyond Standard Model (BSM) theories but they fail to satisfy V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' at large Λ including the scenario of complex triplet scalar with hypercharge 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Hence, alternate scenario can be considered where the new physics appears much above the Electroweak scale, and at low energy it emerges as Standard Model Effective Field Theory (SMEFT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In this literature, we consider some specific BSM scenarios to appear at a large scale such that at low energy we get the Beyond Standard Model Effective Field Theory (BSM- EFT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We found that the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' satisfies easily if the BSM is type-II seesaw model with complex triplet scalar (Y = 1) compared to the other extensions in the BSM-EFT framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We examine the model parameter dependence of the Wilson Coefficients (W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=') in detail and show that the cancellation of the Wilson Coefficients appearing in the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' is highly dependent on some specific values of the model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 1 Introduction The smallness of the observed Higgs mass is confirmed by the experiments [1,2] at the Large Hadron Collider (LHC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' However, in the Standard Model (SM) of particle physics, the scalar mass (mass of Higgs boson) is not protected by any symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Hence, if SM is valid upto a large scale, Planck scale, the Higgs mass suffers from quadratic divergence (∼ Λ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In order to ensure that the mass of the Higgs boson is small, one has to consider a very large fine tuning in the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' A way to ensure that the Higgs mass does not get large correction at a higher scale is coined as Veltman Condition (V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=') [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' checks if the sum of all quadratically divergent terms coming from the self energy diagrams of the Higgs boson are either zero or very small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' On the other hand, experiments such as the Large Hadron Collider (LHC) is pushing the New Physics (NP) scale towards > 1 TeV and the Veltman Criteria is not possible to satisfy in the SM, as it demands Λ to be less than 760 GeV [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Simple extensions of SM has been studied in literature [4–10], where the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' is valid but only in some region of parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Overall, there are two main concerns in these models: (1) These theories encounter different problems at large scale, such as the potential becomes unstable leading 1jaydebphysics@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='com 2nilanjana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='kumar@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='com 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='05524v1 [hep-ph] 13 Jan 2023 to the invalidity of the theory beyond that scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' (2) The non observation of the Beyond Standard Model (BSM) particles at LHC is pushing their masses above TeV scale [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' One may assume that SM is valid upto certain scale (Λ) and above that scale some unknown symmetry appears to protect the Higgs mass, then the Higgs mass can be stabilised and the fine tuning problem can also be addressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' For examples, in the Composite Higgs Scenario [12], where the Higgs is dissolved in higher degrees of freedom above the symmetry breaking scale or in Supersymmetric theories [13], where the bosonic and fermionic degrees of freedom cancels out exactly – the Higgs mass is maintained to be finite and small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' However these theories also can not avoid certain amount of fine tuning [14,15] coming from several sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' However, the none of these theories are observed at LHC and other experiments so far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' These observations raise the question that what if the new physics lie at a very large scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In such a scenario, SM can emerge as an Effective Field Theory (SMEFT) [16] by integrating out the dynamics of the larger theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The Information of the heavy particles appearing in the loop are absorbed in the higher dimensional operators in the Effective Field Theory (EFT) and the theory is invariant under SM symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Ref [17] has shown that the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' can be satisfied in the SMEFT framework by including the higher dimensional operators and their Wilson Coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Only a few of the operators are relevant to the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' and they play a major role in satisfying the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In this paper, we take one step forward and ask this question what if the theory at a very high scale (Λ) is governed by the larger symmetries, and how they affect the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We adopt the Beyond Standard Model Effective Field theory (BSM-EFT) [18] approach, which has been studied previously in Ref [18–24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In BSM-EFT the Lagrangian becomes invariant under the particular BSM model in consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The motivation to study the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' in BSM-EFT framework is two fold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 1) We can specifically check how many higher dimensional operators are allowed by the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 2) We can express the Wilson Coefficients in terms of the model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Hence, the sign dependence of the W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.’s come naturally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We begin with simple BSM scenarios (in BSM-SMEFT) such as, scalar singlet, doublet and triplets (real or complex).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Remarkably, we found that among these models, it is possible to generate all the SMEFT operators that contributes to the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' in the complex scalar triplet model with Y = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' This model makes the cancellation easier in V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' with less fine tuning than the other scenarios3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' This particular model is well motivated in literature from different aspects such as: 1) Neutrino mass generation through the see-saw mechanism [25], 2) type-II Leptogenesis scenario [26] 3) Enhancement of the h → γγ branching ratio [27] etc, among many other [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Hence we pursue this model only in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In Section 2, we show how the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' depends on the SMEFT operators in the WARSAW basis [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In Section 3, we discuss some specific models in the BSM-EFT scenario, and express the Wilson coefficients of Y = 1 complex scalar triplet model in terms of the model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In Section 4, we show how it is possible to satisfy the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' by exact cancellation of the Wilson Coefficients at different scale and interpret the result in terms of the model parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Then in Section 5 we conclude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 3Even type I and type II seesaw models does not generate all these operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Moreover a recent study [22] has also shown that these models are also not favored from the fact that the radiative electroweak symmetry breaking can not be triggered even at the Planck scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 2 2 SMEFT operators in Veltman Criteria The physical mass of the Higgs in the Standard Model can be written in terms of the bare mass term mh(0) and the higher-order self-energy corrections: m2 h = m2 h(0) + δm2 h = m2 h(0) + Log Div.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Term + Quadratic Div.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Term + Finite terms, (1) where the assumption is that the SM is valid upto the scale Λ and the correction terms are coming from the loop diagrams involving scalars, fermions and bosons in the loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The d = 4 potential in the Standard Model in terms of Higgs doublet (H) is V (H) = −m2 HH†H + λ(H†H)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' (2) This leads to the correction to the higgs mass and the quadratic divergent contribution is, (δm2 h)SM = Λ2 16π2 (6λ + 9 4g2 W + 3 4g2 Y − 6y2 t ), (3) where, gY and gW are the U(1)Y and SU(2)L gauge couplings respectively and gt = 2mt/v is the top quark Yukawa coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Here we neglect couplings of the lighter quarks and Λ is the cut-off scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The Veltman Condition (V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=') demands that δm2 h ∼ 0 or at least controllably small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' With the observed Higgs mass at 125 GeV, the condition to make δmh ∼ 0 demands Λ < 760 GeV, which is already ruled out by LHC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' One way to solve this problem is to introduce new particles, which can contribute in the loops and soften the fine tuning by ensuring exact cancellation or partial as we have already discussed in the introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' A popular way to address this problem is to consider the effects of the higher dimensional operators in the EFT framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Let us assume that the New Physics (NP) exists at a very high scale Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The effect of NP can be effectively integrated out at Λ and this will effectively give us SM, plus some effective operators involving only the SM fields, which holds through out the low energy scale, otherwise known as the Standard Model Effective Field Theory (SMEFT) [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The Lagrangian, which incorporates dimension six SMEFT operators in addition to the Standard Model dimension four operators, can be expressed as, L = ∑ i C4iQ4i + 1 Λ2 ∑ i C6iQ6i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' (4) In contrast to C4i, which is the only function of the parameters linked to the degrees of freedom in the Standard Model, C6i are the Wilson Coefficients, which are functions of the integrated out dynamics at Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' These operators can be expanded at any choice of basis, for example, HISZ basis [30], Warsaw basis [29,32], SILH basis [31] etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The set of dimension six operators that involves Higgs in Warsaw basis are: QH = (H†H)3, QHD = (H†DµH)∗(H†DµH), QH◻ = (H†H) ◻ (H†H) QHB = (H†H)BµνBµν, QHW = (H†H)W a µνW a,µν, QGG = (H†H)GA µνGA,µν QHWB = (H†τaH)BµνW a µν (5) It can be shown that the last operator does not contribute Higgs self energy correction [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The first operator will also not contribute at one-loop level as the Higgs does not develop a vev at Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' There can be the appearance of the operators involving the gluons of the form QGG = (H†H)GA µνGA,µν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' However, while considering BSM-EFT framework with heavy scalars, this operator does not contribute as scalars 3 do not carry any color charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Note that, these operators can be written in any basis, for example Ref [17] choose the HISZ basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We choose the Warsaw basis because it is self consistent at one loop [32,33] and easier to check the running of the Wilson coefficients in Warsaw basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The correction to the Higgs mass from the higher order terms in the Lagrangian is given by (δm2 h)total = Λ2 16π2 ∑ i fi(C4i,C6i) + Λ2 (16π2)2 ∑ i gi(C4i,C6i) (6) Here fi and gi are one loop and two loop correction to the Higgs mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=', δm2 h ∼ 0 translates into f(C4i,C6i),g(C4i,C6i) ∼ 0 (7) The coefficients, C4i and C6i are function of Λ and the model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Hence Eq:6 can be written in terms of the SM and higher dimension operators contribution as, (δm2 h)total ≡ (δm2 h)SM(fi(C4i),gi(C4i)) + (δm2 h)HO(fi(C6i),gi(C6i)) (8) Also, it has been shown in Ref [17] that at d ≥ 8, the SMEFT operators are not able to produce any Λ6 divergence, which will produce any effective Λ2 divergence while calculating the self energy correction of Higgs mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' There are studies in the literature, where the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C in terms of EFT has been studied in detail [17,34,35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In particular it has been shown in Ref: [17] that it is possible to satisfy the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C for appropriate values and sign of the Wilson coefficients at large Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 3 BSM-EFT with Complex Scalar Triplet In the above section, we see that only four operators are involved in the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Now, we assume that the new physics at a high scale follow certain symmetries of a BSM model which effectively produces SM as an EFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In this BSM-EFT framework, these 4 operators may or may not be possible to generate at one loop, depending on the underlying symmetry of the model at scale Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In Table: 1 we present if these 4 operators can be generated at one loop in some simple BSM-EFT cases with additional scalar(s) or not 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' For the calculation, we have implemented the Lagrangian of each model in CoDEx [36,37] and generated the Wilson coefficients as an output 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Among all popular SM extensions, we have found that BSM-EFT with complex scalar triplet will easily address the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C, as it generates all four Wilson Coefficients at one loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In other models, the cancellation will be harder to achieve as the number of operators are less than four.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' For example in 2HDM scenario and real scalar singlet + triplet model, only three operators can be generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Whereas, in complex scalar singlet model, only 2 operators are generated and the cancellation will be hard to obtain (hence large fine tuning) in these models compared to the complex scalar triplet model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Even larger fine tuning will be unavoidble for the real scalar singlet model as it generates only one operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The complex scalar triplet with additional doublet also can generate these four operators but we examine the minimal scenario only with complex scalar triplet model in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 4Note that we are not checking non scalar extensions of SM because, the sign of the top-loop contribution (dominant contribution) or rather fermionic contribution is opposite to the other diagrams with a gauge boson or a scalar in the loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Therefore, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' is hard to solve by adding non scalar particles such as vector-like quarks or fermions, additional gauge bosons etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 5We have also cross checked our result with Matchmakereft [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 4 Model Quantum No QHD QHB QHW QH◻ Real Scalar Singlet (1,1,0) \x13 \x17 \x17 \x17 Real Scalar Triplet (1,3,0) \x17 \x17 \x13 \x13 Complex Scalar Triplet (1,3,1) \x13 \x13 \x13 \x13 Complex scalar doublets (2HDM) (1,2,±1/2) \x13 \x17 \x13 \x13 Real Scalar Singlet + (1,1,0) \x13 \x17 \x13 \x13 Real Scalar Triplet (1,3,0) Complex Scalar Triplet + (1,3,1) \x13 \x13 \x13 \x13 Complex Scalar Doublet (1,2,1/2) Table 1: SMEFT operators in Warsaw basis in different BSM-EFT scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Let us consider that beyond the scale Λ, there exists a heavy complex triplet, ∆, with weak hypercharge Y = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The most general renormalizable tree-level scalar potential of such a model is given by V (H,∆) = −m2 H (H†H) + M2Tr[∆†∆] + (µ∆HT iσ2∆+H + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='c) + λ(H†H) 2 + λ1 (H†H)Tr[∆†∆] + λ2 (Tr[∆†∆]) 2 + λ3Tr[(∆†∆)2] + λ4 (H†∆∆†H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' (9) The extra Yukawa term for neutrino mass generation is, LY = y∆ℓT iCiσ2∆ℓ + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' (10) Here the trilinear coupling µ∆ can be taken as positive by absorbing its phase into Φ and ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The total Lagrangian is, L = LY − V (H,∆), (11) The detail of this model is summarized in ‘Model Description’ part of the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The dimension six operators the Warsaw basis, as listed in Eq:5, can be expanded and the calculation of the symmetry factors are shown in the ‘Calculation’ part of the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Hence, the Higgs mass correction in terms of W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.’' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='s is found to be,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' (δm2 h)BSM = Λ2 16π2 ( − 3CHD + 12CH◻ + 9CHW + 3CHB) + Λ2 (16π2)2 (54CH − 9 2(g2 Y + 3g2 W )CHD + 108g2 W CHW ) (12) Which leads to the total correction to the Higgs mass to be,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='δm2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='h = (δm2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='h)SM + (δm2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='h)BSM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='(13) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='We found the the following expressions of the Wilson Coefficients appearing in one loop contribution ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='in (δm2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='h)BSM: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='CHD ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='= ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='g4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='Y ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='320π2 + 4µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='M2 − ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='λ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='24π2 + 11g2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='Y µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='24π2M2 − ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='8µ4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='3π2M4 + λ4µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='6π2M2 + 3λµ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='8π2M2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='(14) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='CH◻ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='= ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='g4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='W ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='1920π2 + 2µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='M2 − ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='λ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='16π2 − λ1λ4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='16π2 − ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='λ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='192π2 − g2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='W µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='96π2M2 + ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='11g2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='Y µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='96π2M2 − ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='49µ4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='12π2M4 + λ1µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='8π2M2 + ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='λ4µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='48π2M2 + 3λµ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='4π2M2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='(15) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='CHB ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='= ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='g2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='Y λ1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='32π2 + g2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='Y λ4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='64π2 + 11g2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='Y µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='64π2M2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='(16) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='CHW ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='= ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='g2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='W λ1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='48π2 + g2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='W λ4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='96π2 + 25g2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='W µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='∆ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='192π2M2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' (17) Here, M is the mass of the heavy triplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' For the theory to be valid, it is sufficient to assume that M is greater than Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We assume the order of magnitude to be the same for M and Λ in our calculation as a limiting scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' For M >> Λ, the W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.’s will obtain smaller values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 4 Result We consider the one loop correction to the Higgs mass at first and fix two benchmark scenarios at large scales, such as 100 TeV, 106 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In Fig: 1 we show the model parameter space of λ1 and λ4, for which quadratic divergence cancels out exactly, making δm2 h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The SM input parameters, such as (gW , yt, gY , λ) are determined at the benchmark scales by solving two loop Renormalized Group Equation (RGE)’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' λ1 and λ4 are varied in such a way that the Wilson Coefficients obey the perturbative limit and the running of the Wilson Coefficients from Λ to the EW scale is not varied much.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Note that, the tree level couplings (λ and µH) also get shifted due to the higher dimensional operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The parameter λ can not be more than O(1) and this puts an upper limit on the quantity, µ2 ∆ 2M2 < O(1), where µ∆ = √ 2v∆M2 v2 H , in the limit of large masses of the triplet (M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Also, recent precission measurements of the ρ parameter gives ρ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='00038 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='00020, resulting in v∆ < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='56 [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Figure 1: Variation of λ1 and λ4 with µ∆ at two benchmark values of Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 6 6 =100 GeV = 5*104 GeV 3 = 105 GeV 0 3 A=100TeV 6 50 25 0 25 50 入46 =100 GeV =5*108GeV 3 = 109 GeV 0 3 Λ=10% Tev 6 50 25 0 25 50 入4From Fig: 1, we can see that the parameter space of (λ1, λ4) is very much constrained from the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Note that, both positive and negative values of λ1 and λ4 are allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The green line represents the highest possible value of µ∆, which comes from µ2 ∆ 2M2 ∼ O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' only satisfies over the thin lines for different values of µ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The nature of the plots is highly dependent on the values of µ∆, because the Wilson coefficients have (µ∆/M)2 and (µ∆/M)4 dependence with additional suppression of 1/16π2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The freedom to choose the W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C’s in terms of parameters λ1, λ4 and µ∆, allows the exact cancellation even at a very large scale ( Λ = 106 TeV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The small change in parameter space is due to the running of the SM parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Hence we found that the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C is insensitive to the scale Λ, and the fine tuning is appearing only due to the precession of the numbers that the parameters take, which is negligible6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Figure 2: Variation of the Wilson Coefficients with model parameter λ4 In Fig: 2, we show the variation of the Wilson Coefficients with the model parameter λ4 at 100 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The corresponding value(s) of λ1 can be inferred form Fig: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The Wilson coefficients show similar behaviour for the othe benchmark case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' For CHD and CH◻, negative values are more preferred, whereas, for CHW and CHB, both positive and negative values are allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' However, when λ4 is negative, all coefficients are negative mostly, except for some values of the CHD and CH◻.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Again, when λ4 is positive, CHW and CHB are always positive but CHD and CH◻ are mostly negative except for some values as shown in Fig: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Thus, it is clearly visible that the cancellation among the Wilson coefficients are not ad-hoc in V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=', but are controlled by the model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We have also implemented the two loop 6Note that, for other models, where the number of Wilson Coefficient is less than 4 can be generated, the exact cancellation will be harder to obtain and the amount of fine tuning will also be very high compared to this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 7 10 = 100 GeV = 5104 GeV 5 μ = 105 GeV CHD 5 Λ= 100 TeV 10 50 25 0 25 50 入42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='5 =100 GeV = 5*104 GeV 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='5 μ = 105 GeV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='5 CH 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='5 A=100TeV 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='5 50 25 0 25 50 入40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='02 =100 GeV M = 5*104 GeV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='01 M = 105 GeV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='01 Λ= 100 TeV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='02 50 25 0 25 50 入40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='050 =100GeV = 5*104GeV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='025 M = 105 GeV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='025 Λ = 100 TeV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='050 50 25 0 25 50 入4contribution to Higgs mass correction and in V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Due to the extra suppression by (1/16π2), the effect is not visible, hence we do not show that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' \uf772HD \uf772H \uf3a4 100 104 106 108 8 6 4 2 0 Λ(GeV) λ1 = 4, λ4 = 40, μΔ = 1000 GeV \uf772HW \uf772HB 100 104 106 108 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='015 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='020 Λ(GeV) λ1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='01, λ4 = 40, μΔ = 1000 GeV Figure 3: Running of the Wilson Coefficients from Λ = 106 TeV to the cut-off scale for one set of model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We have kept the value of µ∆ to be fixed at 1 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We have also checked the running of the Wilson coefficients from the effective scale Λ to the electroweak scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We show the running of the Wilson coefficients in Fig: 3 for a particular choice of the model parameters, λ1 and λ4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We choose λ1 = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='0 and λ4 = 40 as an input parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' This particular choice of parameter represents the maximum possible value of the model parameters as can be seen in Fig: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We found that, the values of these W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.’s do not change much and also the sign does not change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The conclusion remains same for other allowed values of λ1 and λ4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The values of W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' (Ci(1TeV)2/Λ2) are highly constrained at the EW scale [40] from various experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The values of Wilson coefficients (as in Fig: 2,Fig: 3), for which the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' is satisfied, is well within the current experimental limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 5 Conclusion The Veltman Condition can not be satisfied within the framework of the Standard Model because of significant quadratic divergences to the Higgs self-energy correction if the cutoff scale Λ is ∼ 1 TeV or higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' However, in addition to the dimension four operators from the Standard Model, we have also included dimension six operators whose contributions to the Higgs mass correction result from integrating out the heavy triplet scalar with hypercharge one in terms of the SMEFT operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We show how the quadratic divergence of the Higgs self-energy vanishes in this particular model due to the cancellation among the SM parameters and the Wilson Coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We have shown the relevant SMEFT operators which contributes in the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=', and expressed them in terms of the model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Hence, the sign of the Wilson Coefficients are not ad-hoc, it is driven by the larger theory, which is a heavy triplet scalar in our case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We found that, in other models the cancellation is harder to achieve because some of the operators are absent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In other words, one has to allow for a minimum fine tuning in order to generate the model parameter space which is allowed by the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' However, the values of the Wilson Coefficients will be different in every model, as it is controlled by the specific model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' In order to achieve the Veltman Condition, it should be noted that the contributions from two par- ticular dimension six operators QHD and QH◻ play a dominating role in cancelling out the quadratic 8 divergences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' However, this may or may not be the case in other models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We have observed that for energy scales Λ = 100 TeV and 106 TeV, the cancellation is almost similar, when the W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C’s are expressed in terms of λ1 and λ4 for a given µ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The minimal change in the parameter space is mainly due to the running of the SM parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' If we introduce some relaxation in the V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=', by allowing some amount of fine tuning, the model parameter space will surely enlarge, but it will get narrower with the increasing values of Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Thus, the Veltman Condition can be easily satisfied in the framwork of effective field theory, when a scalar triplet exists at a very large scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The study of this model as an Effective Field Theory can also be useful to revisit the Type II leptogenesis scenario, where it will be possible to generate specific dimension six terms which are allowed by the symmetries of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Acknowledgements: JD acknowledges the Council of Scientific and Industrial Research (CSIR), Government of India, for the SRF fellowship grant with File No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 09/045(1511)/ 2017-EMR-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' JD also would like to acknowledge Research Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' SERB/CRG/004889/SGBKC/2022/04 of the SERB, India, for partial financial support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The work of NK is supported by Department of Science and Technology, Government of India under the SRG grant, Grant Agreement Number SRG/2022/000363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' We also thank Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Anirban Kundu and Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Supratim Das Bakshi for useful discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 6 Appendix Model Description In the type-II seesaw model, the scalar sector is extended by a complex scalar triplet(∆) with hypercharge 1, in addition to the Higgs doublet (H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Explicitly, H (1,2,+1/2) = (φ+ φ0), ∆(1,3,+1) = (∆+/ √ 2 ∆++ ∆0 −∆+/ √ 2) (18) with the neutral components: φ0 = vH + h + iφ3 √ 2 , ∆0 = v∆ + δ + iξ √ 2 (19) The numbers in the parentheses represent the charges of SU(3)C × SU(2)L × U(1)Y gauge group of the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' The kinetic terms corresponding to the scalar fields are given as Lkin ⊃ (DµH)†DµH + Tr[(Dµ∆)†(Dµ∆)], (20) with the covariant derivatives DµH = ∂µH − igY 2 W a µσaH − igW 2 BµH, Dµ∆ = ∂µ∆ − igY 2 Tr[W a µσa,∆] − igW 2 Bµ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' (21) Here σa (a = 1, 2, 3) are the Pauli spin matrices and gW and gY are the gauge couplings associated with SU(2)L and U(1)Y gauge group respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 9 Calculation The dimension six SMEFT operators which contribute Higgs mass correction either at one-loop or two-loop level in this model can be written upto a total derivative as,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' QHD = (H+DµH)∗(H+DµH) ⊃ (∂µH†)HH† (∂µH†) + [g2 W 4 σaσbH†W a µHH†W µbH + g2 Y 4 H†BµHH†BµH] QH◻ = (H+H) ◻ (H+H) = −∂µ (H†H)∂µ (H†H) QHW = (H+H)W a µνW a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content='µν ⊃ 2H†[σa (∂µW a ν )σb (∂µW νb) − σa (∂µW a ν )σb (∂νW µb)]H + g2 W σafabcσpfpqrH†W b µW c νW µqW νrH QHB = (H+H)BµνBµν ⊃ 2H†[∂µBν∂µBν − ∂µBν∂νBµ]H QH = (H†H)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' (22) Note that only momentum dependent vertices can generate quartic divergence at one-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Pos- sible Feynman diagrams originating from these terms are similar to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' References [1] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' Aad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E5T4oBgHgl3EQfRw7N/content/2301.05524v1.pdf'} +page_content=' 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