A new and trivial CP symmetry for extended $A_4$ flavor

Abstract

The combination of ${\nu }_{\mu }$-${\nu }_{\tau }$ exchange together with CP conjugation in the neutrino sector (known as ${\mathrm{CP}}^{\mu \tau }$ symmetry or $\mu \tau$-reflection) is known to predict the viable pattern: ${\theta }_{23}=45^{\circ }$, maximal Dirac CP phase and trivial Majorana phases. We implement such a CP symmetry as a new CP symmetry in theories with $A_4$ flavor. The implementation in a complete renormalizable model leads to a new form for the neutrino mass matrix that leads to further predictions: normal hierarchical spectrum with lightest mass and $m_{\beta \beta }$ ($0\nu \beta \beta$) of only few meV, and either ${\nu }_1$ or ${\nu }_2$ has opposite CP parity. An approximate $L_{\mu }-L_{\tau }$ symmetry arises naturally and controls the flavor structure of the model. The light neutrino masses are generated by the extended seesaw mechanism with 6 right-handed neutrinos (RHNs). The requirement of negligible one-loop corrections to light neutrino masses, validity of the extended seesaw approximation and not too long-lived BSM states to comply with BBN essentially restricts the parameters of the model to a small region: three relatively light right-handed neutrinos at the GeV scale, heavier neutrinos at the electroweak scale and Yukawa couplings smaller than the electron Yukawa. Such a small Yukawa couplings render these RHNs unobservable in terrestrial experiments.

Comments: 23pp, 7 figs; v2: published version with small updates in text