Renormalization Group Running of Lepton Mixing Parameters in See-Saw Models with $S_4$ Flavor Symmetry

TL;DR

This paper investigates how neutrino mixing parameters predicted by $S_4$ flavor models evolve under renormalization group effects, revealing small corrections for some angles and significant deviations for others, constraining neutrino spectra.

Contribution

It provides a detailed analysis of the renormalization group running of lepton mixing parameters in $S_4$ models, highlighting the impact of $ aneta$ and neutrino hierarchy on the evolution.

Findings

Quantum corrections to atmospheric and reactor angles are negligible.

Solar mixing angle deviations depend on $ aneta$ and hierarchy.

Inverted hierarchy is disfavored at large $ aneta$.

Abstract

We study the renormalization group running of the tri-bimaximal mixing predicted by the two typical $S_4$ flavor models at leading order. Although the textures of the mass matrices are completely different, the evolution of neutrino mass and mixing parameters is found to display approximately the same pattern. For both normal hierarchy and inverted hierarchy spectrum, the quantum corrections to both atmospheric and reactor neutrino mixing angles are so small that they can be neglected. The evolution of the solar mixing angle $\theta_{12}$ depends on $\tan\beta$ and neutrino mass spectrum, the deviation from its tri-bimaximal value could be large. Taking into account the renormalization group running effect, the neutrino spectrum is constrained by experimental data on $\theta_{12}$ in addition to the self-consistency conditions of the models, and the inverted hierarchy spectrum is disfavored for large $\tan\beta$. The evolution of light-neutrino masses is approximately described by a common scaling factor.