Radiative and Seesaw Threshold Corrections to the $S_3$ Symmetric Neutrino Mass Matrix

TL;DR

This paper investigates how radiative corrections and seesaw threshold effects influence the neutrino mass matrix with $S_3$ symmetry, showing that these effects can align theoretical predictions with experimental data at low energies.

Contribution

It provides a systematic analysis of radiative and seesaw threshold corrections to the $S_3$ symmetric neutrino mass matrix at high energy scales, highlighting their impact on neutrino parameters in SM and MSSM.

Findings

In the SM, all three mixing angles and atmospheric mass difference match current data at low energy.

In the SM, the solar mass squared difference exceeds experimental bounds at low energy.

In MSSM with large tanβ, seesaw threshold effects are crucial for matching neutrino parameters with observations.

Abstract

We systematically analyze the radiative corrections to the $S_3$ symmetric neutrino mass matrix at high energy scale, say the GUT scale, in the charged lepton basis. There are significant corrections to the neutrino parameters both in the Standard Model (SM) and Minimal Supersymmetric Standard Model (MSSM) with large tan$\beta$, when the renormalization group evolution (RGE) and seesaw threshold effects are taken into consideration. We find that in the SM all three mixing angles and atmospheric mass squared difference are simultaneously obtained in their current 3$\sigma$ ranges at the electroweak scale. However, the solar mass squared difference is found to be larger than its allowed 3$\sigma$ range at the low scale in this case. There are significant contributions to neutrino masses and mixing angles in the MSSM with large tan$\beta$ from the RGEs even in the absence of seesaw threshold corrections. However, we find that the mass squared differences and the mixing angles are obtained in their current 3$\sigma$ ranges at low energy when the seesaw threshold effects are also taken into account in the MSSM with large tan$\beta$.