Radiative Corrections to the Solar Lepton Mixing Sum Rule

TL;DR

This paper examines how radiative corrections influence the solar lepton mixing sum rule within the MSSM framework, analyzing the RG effects on the CP phase and mixing angles for different neutrino mixing patterns.

Contribution

It provides a detailed analysis of RG running effects on the solar lepton mixing sum rule and assesses the compatibility of various mixing scenarios with experimental data.

Findings

Radiative corrections can enhance the compatibility of the BM scenario with data.

RG effects broaden the posterior distribution of the CP phase δ.

The TBM and GR scenarios are less favored after considering radiative corrections.

Abstract

The simple correlation among three lepton flavor mixing angles $(\theta^{}_{12}, \theta^{}_{13}, \theta^{}_{23})$ and the leptonic Dirac CP-violating phase $\delta$ is conventionally called a sum rule of lepton flavor mixing, which may be derived from a class of neutrino mass models with flavor symmetries. In this paper, we consider the solar lepton mixing sum rule $\theta^{}_{12} \approx \theta^{\nu}_{12} + \theta^{}_{13} \cos \delta$, where $\theta^\nu_{12}$ stems from a constant mixing pattern in the neutrino sector and takes the value of $\theta^\nu_{12} = 45^\circ$ for the bi-maximal mixing (BM), $\theta^\nu_{12} = \tan^{-1}(1/\sqrt{2}) \approx 35.3^\circ$ for the tri-bimaximal mixing (TBM) or $\theta^\nu_{12} = \tan^{-1}\left[2/(\sqrt{5} + 1)\right] \approx 31.7^\circ$ for the golden-ratio mixing (GR), and investigate the renormalization-group (RG) running effects on lepton flavor mixing parameters when this sum rule is assumed at a superhigh-energy scale. For illustration, we work within the framework of the minimal supersymmetric standard model (MSSM), and implement the Bayesian approach to explore the posterior distribution of $\delta$ at the low-energy scale, which becomes quite broad when the RG running effects are significant. Moreover, we also discuss the compatibility of the above three mixing scenarios with current neutrino oscillation data, and observe that radiative corrections can increase such a compatibility for the BM scenario, resulting in a weaker preference for the TBM and GR ones.