Soft $A_4 \to Z_3$ Symmetry Breaking and Cobimaximal Neutrino Mixing

TL;DR

This paper introduces a model where soft breaking of $A_4$ symmetry to $Z_3$ lepton triality enables the realization of cobimaximal neutrino mixing with minimal deviations, addressing a longstanding issue in $A_4$ models.

Contribution

It presents a novel $A_4$ symmetry breaking scheme that achieves cobimaximal neutrino mixing with small, calculable deviations, solving a key technical problem in renormalizable $A_4$ models.

Findings

Successfully implements $A_4$ to $Z_3$ breaking with dimension-three terms.

Achieves cobimaximal neutrino mixing with minimal deviations.

Provides a solution to a long-standing technical challenge in $A_4$ models.

Abstract

I propose a model of radiative charged-lepton and neutrino masses with $A_4$ symmetry. The soft breaking of $A_4$ to $Z_3$ lepton triality is accomplished by dimension-three terms. The breaking of $Z_3$ by dimension-two terms allow cobimaximal neutrino mixing $(\theta_{13} \neq 0, \theta_{23} = \pi/4, \delta_{CP} = \pm \pi/2)$ to be realized with only very small finite calculable deviations from the residual lepton triality. This construction solves a long-standing technical problem inherent in renormalizable $A_4$ models since their inception.