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Renormalization group evolution induced breaking of $μ-τ$ reflection symmetry in MSSM with effects of variation of $tanβ$

Chandan Kumar Borah, Chandan Duarah

Abstract

We study the renormalization group (RG) evolution induced breaking of $μ$--$τ$ reflection symmetry in the Minimal Supersymmetric Standard Model (MSSM), with a special focus on the effects of varying $\tanβ\equiv v_u/v_d$, the ratio of MSSM Higgs vacuum expectation values. Starting from an exact $μ$--$τ$ reflection symmetry imposed at a high flavor symmetry scale $Λ_{\text{FS}}$, we run the complete set of coupled RGEs for neutrino masses, mixing angles, and CP-violating phases down to the electroweak scale, imparting perturbation to the symmetry. We consider a specific value of the SUSY breaking scale, $Λ_s=7\ TeV$ during the run. By choosing suitable free parameters at the high-energy scale, we reproduce the low-energy experimental constraints on neutrino observables consistent with $3ν$ global analysis data. We then examine how the breaking of $μ$--$τ$ reflection symmetry is influenced by different values of $\tanβ$, considering three benchmark choices. In addition, the analysis is performed for both normal ordering (NO) and inverted ordering (IO) of neutrino masses to highlight potential differences in their RG running behavior.

Renormalization group evolution induced breaking of $μ-τ$ reflection symmetry in MSSM with effects of variation of $tanβ$

Abstract

We study the renormalization group (RG) evolution induced breaking of -- reflection symmetry in the Minimal Supersymmetric Standard Model (MSSM), with a special focus on the effects of varying , the ratio of MSSM Higgs vacuum expectation values. Starting from an exact -- reflection symmetry imposed at a high flavor symmetry scale , we run the complete set of coupled RGEs for neutrino masses, mixing angles, and CP-violating phases down to the electroweak scale, imparting perturbation to the symmetry. We consider a specific value of the SUSY breaking scale, during the run. By choosing suitable free parameters at the high-energy scale, we reproduce the low-energy experimental constraints on neutrino observables consistent with global analysis data. We then examine how the breaking of -- reflection symmetry is influenced by different values of , considering three benchmark choices. In addition, the analysis is performed for both normal ordering (NO) and inverted ordering (IO) of neutrino masses to highlight potential differences in their RG running behavior.

Paper Structure

This paper contains 6 sections, 18 equations, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Renormalization group evolution of neutrino parameters and the role of $\tan\beta$
  3. Numerical results
  4. Normal Order ($m_1<m_2<m_3$)
  5. Inverted Order ($m_3<m_1<m_2$)
  6. Summary and discussion

Figures (8)

  • Figure 1: Evolution of mass eigenvalues and mixing angles with energy scale for NO and case-I with three different values of $\tan\beta$. Solid and dashed portions of each curve represent the evolution in the MSSM and SM regions respectively. Magenta , green and red colors respectively stands for $\tan\beta=10,\ 30\ \text{and}\ 58$.
  • Figure 2: Evolution of CP phases with energy scale for NO and case-I with three different values of $\tan\beta$. Solid and dashed portions of each curve represent the evolution in the MSSM and SM regions respectively. Magenta , green and red colors respectively stands for $\tan\beta=10,\ 30\ \text{and}\ 58$.
  • Figure 3: Evolution of mass eigenvalues and mixing angles with energy scale for NO and case-II with three different values of $\tan\beta$. Solid and dashed portions of each curve represent the evolution in the MSSM and SM regions respectively. Magenta, green and red colors respectively stand for $\tan\beta=10,\ 30\ \text{and}\ 58$.
  • Figure 4: Evolution of CP phases with energy scale for NO and case-II with three different values of $\tan\beta$. Solid and dashed portions of each curve represent the evolution in the MSSM and SM regions respectively. Magenta , green and red colors respectively stands for $\tan\beta=10,\ 30\ \text{and}\ 58$.
  • Figure 5: Evolution of mass eigenvalues and mixing angles with energy scale for IO and case-I with three different values of $\tan\beta$. Solid and dashed portions of each curve represent the evolution in the MSSM and SM regions respectively. Magenta , green and red colors respectively stands for $\tan\beta=10,\ 30\ \text{and}\ 58$.
  • ...and 3 more figures