$A_4$ Flavor Model for Deviation in $\mu -\tau$ Reflection Symmetry with Type-I+II Seesaw Extensions

Abstract

In this work, we propose a theoretical scenario for deviation from $\mu -\tau$ reflection symmetry explaining non-maximal values of atmospheric mixing angle ($\theta _{23}$). In fact, $\mu -\tau$ reflection symmetry of neutrino mass matrix predict maximal $\theta _{23}$ ($=45^o$) and maximal CP violation i.e. Dirac CP phase ($\delta =\pm \frac{\pi }{2}$). We propose A$_4$ symmetry based deviation in $\mu -\tau$ reflection symmetry and investigate its phenomenology using Type-I+II seesaw mechanism for neutrino mass generation. We have obtained deviations from the predictions of $\mu -\tau$ reflection symmetry. The model satisfies the neutrino oscillation data for normal hierarchy of neutrino masses while inverted hierarchy is ruled out. We have, also, obtained predictions on neutrinoless double beta decay ($0\nu \beta \beta$) amplitude, $M_{ee}$.