Importance of generalized $\mu \tau$ symmetry and its CP extension on neutrino mixing and leptogenesis

Abstract

Within the framework of residual symmetry, two ${\mathbb{Z}}_2$ type associate $\mu \tau$ interchange symmetries robustly constrain the Dirac CP phase $\delta$ in a model independent way. Both of them predict simultaneous maximality of $\delta$ and the atmospheric mixing angle ${\theta }_{23}$. We show how these well known correlations will be changed if we generalize the $\mu \tau$ interchange symmetry to a $\mu \tau$ 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 $\mu \tau$ interchange. In addition, the present neutrino data on $\delta$ and ${\theta }_{23}$ can be explained better by the mixing symmetry. After discussing the impact of the $\mu \tau$ 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 $\delta$ and the mixing angles ${\theta }_{ij}$. Next we discuss in particular, the `three flavour regime' of leptogenesis within the CP extended framework and show, unlike the ordinary CP extended $\mu \tau$ interchange symmetry, a resonant leptogenesis is possible due the generalization of $\mu \tau$ interchange to the $\mu \tau$ mixing and the resulting baryon asymmetry always requires a nonmaximal ${\theta }_{23}$ owing to the fact that the baryon to photon ratio ${\eta }_B$ vanishes in the exact limit of ${\theta }_{23}=\pi /4$. This is one of the robust predictions of this framework. The CP extended $\mu \tau$ 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.

arXiv comment33 pages, 14 figures. Version accepted for publication in JHEP

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