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

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.