Viability of exact tri-bimaximal, golden-ratio and bimaximal mixing patterns and renormalization-group running effects

TL;DR

This study investigates whether exact tri-bimaximal, golden-ratio, or bimaximal neutrino mixing patterns can be realized at high energy scales and remain compatible with low-energy experimental data through renormalization-group corrections within the MSSM framework.

Contribution

It provides a comprehensive analysis of the viability of exact neutrino mixing patterns considering RG running effects and current cosmological neutrino mass bounds.

Findings

None of the mixing patterns are viable below the seesaw scale under current neutrino mass bounds.

Relaxing the neutrino mass sum bound allows TBM and GR patterns at 3σ, but not at 1σ.

BM pattern is incompatible regardless of the neutrino mass sum bound.

Abstract

In light of the latest neutrino oscillation data, we examine whether the leptonic flavor mixing matrix can take on an exact form of tri-bimaximal (TBM), golden-ratio (GR) or bimaximal (BM) mixing pattern at a superhigh-energy scale, where such a mixing pattern could be realized by a flavor symmetry, and become compatible with experimental data at the low-energy scale. Within the framework of the Minimal Supersymmetric Standard Model (MSSM), the only hope for realizing such a possibility is to count on the corrections from the renomalization-group (RG) running. In this work we focus on these radiative corrections, and fully explore the allowed parameter space for each of these mixing patterns. We find that when the upper bound on the sum of neutrino masses $\Sigma^{}_\nu \equiv m^{}_1 + m^{}_2 + m^{}_3 < 0.23~\text{eV}$ at the $95\%$ confidence level from Planck 2015 is taken into account, none of these mixing patterns can be identified as the leptonic mixing matrix below the seesaw threshold. If this cosmological upper bound on the sum of neutrino masses were relaxed, the TBM and GR mixing patterns would still be compatible with the latest neutrino oscillation data at the $3\sigma$ level, but not at the $1\sigma$ level. Even in this case, no such a possibility exists for the BM mixing.