Partial $μ-τ$ symmetry from kinetic normalization

TL;DR

This work investigates breaking of approximate μ-τ permutation symmetry through non-canonical lepton kinetic terms induced by higher-dimensional operators. By canonically normalizing the kinetic terms with flavon-induced factors, a complex parameter $k$ links the μ and τ sectors, leading to two key, k-independent constraints on the neutrino mass matrix, including $M_{13}^2 M_{22}=M_{12}^2 M_{33}$. An analytic and numerical analysis shows that, under normal hierarchy with a massless lightest state, the model severely restricts $|V_{\mu3}|$ and pushes the atmospheric angle into the second octant, while inverted hierarchy allows a larger but still constrained region, with predictions favoring higher $|V_{\mu3}|$ values. The results provide a novel kinetic-term-based mechanism for μ-τ breaking with sharp, testable implications for neutrino mixing angles and mass ordering.

Abstract

We consider models with broken $μ$-$τ$ permutation symmetry through higher dimensional operators renormalizing the lepton kinetic terms in the action. We study the consequences on the structure of the neutrino mass matrix and find in particular that the allowed region for the lightest mass in the normal hierarchy plotted as a function of the atmospheric mixing element $|V_{\mu3}|$ is very restricted with the atmospheric mixing angle $θ_{23}$ to lie in the second octant. On the other hand, the corresponding allowed region in the inverted hierarchy regime is less restrictive.

Figures (2)

• Figure 1: Lightest mass as a function of $|V_{\mu3}|$ in the NH ordering.
• Figure 2: Lightest mass as a function of $|V_{\mu3}|$ in the IH ordering.