Combinations of the $\mu$-$\tau$ reflection symmetry and texture zeros in the Dirac neutrino mass matrix of the seesaw model

Abstract

In this paper, we have studied the combinations of texture zeros with the $\mu$—$\tau$ reflection symmetry (which predicts $\theta ^{}_{23} = \pi /4$ and $\delta = \pm \pi /2$) so that the predictive power of the seesaw model can be further improved: in the basis of the right-handed neutrino mass matrix being diagonal, we impose some texture zeros on the Dirac neutrino mass matrix which obeys the $\mu$—$\tau$ reflection symmetry, and then study its phenomenological consequences for the neutrino observables and leptogenesis. We have first performed the study in the general seesaw model with three right-handed neutrinos. Then, to further reduce the free parameters of the seesaw model and thus further improve its predictive power, we have performed the study in the following two simplified scenarios: reducing the general seesaw model to the minimal seesaw model (with only two right-handed neutrinos); combining the $\mu$—$\tau$ reflection symmetry with the TM1 and TM2 mixings.