Perturbative Estimates of Lepton Mixing Angles in Unified Models

TL;DR

This paper develops approximate analytic formulas to estimate lepton mixing angles in unified models, accounting for charged lepton corrections, RG effects, and canonical normalization, especially applied to tri-bimaximal mixing.

Contribution

It introduces simple perturbative formulas for lepton mixing angles that incorporate various high-energy effects, enhancing predictive accuracy in unified models.

Findings

Perturbative formulas accurately estimate lepton mixing angles.

Application to tri-bimaximal mixing reveals specific correction patterns.

Provides a comprehensive analysis of limiting cases and sum rule relations.

Abstract

Many unified models predict two large neutrino mixing angles, with the charged lepton mixing angles being small and quark-like, and the neutrino masses being hierarchical. Assuming this, we present simple approximate analytic formulae giving the lepton mixing angles in terms of the underlying high energy neutrino mixing angles together with small perturbations due to both charged lepton corrections and renormalisation group (RG) effects, including also the effects of third family canonical normalization (CN). We apply the perturbative formulae to the ubiquitous case of tri-bimaximal neutrino mixing at the unification scale, in order to predict the theoretical corrections to mixing angle predictions and sum rule relations, and give a general discussion of all limiting cases.