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 $μ$--$τ$ 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.