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 $({\theta }_{13}\ne 0,{\theta }_{23}=\pi /4,{\delta }_{CP}=\pm \pi /2)$ 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.

Comments: 8 pages, 4 figures