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

Within the framework of residual symmetry, two 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.