Importance of generalized $μτ$ symmetry and its CP extension on neutrino mixing and leptogenesis

Abstract

Within the framework of residual symmetry, two $\mathbb{Z}_2$ type associate $μτ$ interchange symmetries robustly constrain the Dirac CP phase $δ$ in a model independent way. Both of them predict simultaneous maximality of $δ$ and the atmospheric mixing angle $θ_{23}$. We show how these well known correlations will be changed if we generalize the $μτ$ interchange symmetry to a $μτ$ mixing symmetry. In particular, we show that the stringent condition of simultaneous maximality could be relaxed even with a very small departure from the exact $μτ$ interchange. In addition, the present neutrino data on $δ$ and $θ_{23}$ can be explained better by the mixing symmetry. After discussing the impact of the $μτ$ mixing in some realistic neutrino mass models, we show how the proposed mixing could be realized with two simultaneous CP transformations which also lead to novel and testable correlations between $δ$ and the mixing angles $θ_{ij}$. Next we discuss in particular, the `three flavour regime' of leptogenesis within the CP extended framework and show, unlike the ordinary CP extended $μτ$ interchange symmetry, a resonant leptogenesis is possible due the generalization of $μτ$ interchange to the $μτ$ mixing and the resulting baryon asymmetry always requires a nonmaximal $θ_{23}$ owing to the fact that the baryon to photon ratio $η_B$ vanishes in the exact limit of $θ_{23}=π/4$. This is one of the robust predictions of this framework. The CP extended $μτ$ mixing is also a novel example of a low energy effective model that provides an important insight to the off-diagonal terms of the flavour coupling matrix which have usually been neglected in literature to compute the final baryon asymmetry, in particular in the models with flavour symmetries.