A study on a minimally broken residual TBM-Klein symmetry with its implications on flavoured leptogenesis and ultra high energy neutrino flux ratios

We present a systematic study on minimally perturbed neutrino mass matrices which at the leading order give rise to Tri-BiMaximal (TBM) mixing due to a residual Z(2) x Z(2)(mu tau) Klein symmetry in the neutrino mass term of the low energy effective seesaw Lagrangian. Considering only the breaking of Z(2)(mu tau) with two relevant breaking parameters (epsilon(4,6)'), after a comprehensive numerical analysis, we show that the phenomenologically viable case in this scenario is a special case of TM1 mixing. For this class of models, from the phenomenological perspective, one always needs large breaking (more than 45%) in one of the breaking parameters. However, to be consistent the maximal mixing of theta(23), while more than 35% breaking is needed in the other, a range 49.4 degrees-53 degrees and 38 degrees-40 degrees could be probed allowing breaking up to 25% in the same parameter. Thus though this model cannot distinguish the octant of theta(23), non-maximal mixing is preferred from the viewpoint of small breaking. The full Z(2) x Z(2)(mu tau) symmetry leads to a degeneracy in the eigenvalues of right handed (RH) neutrino mass matrices (M-R). Nevertheless, breaking of Z(2)(mu tau) which is also necessary to generate nonzero theta(13) in this model, lifts that degeneracy. Thus unlike the standard N-1-leptogenesis scenario where only the decays and other interactions due to the lightest RH neutrino N-1 are relevant, here all the RH neutrinos contribute to the process of baryogenesis via leptogenesis due to the small mass splitting controlled by the Z(2)(mu tau) breaking parameters. Including flavour coupling effects (In general, which have been partially included in all the leptogenesis studies in perturbed TBM framework), we solve flavour dependent coupled Boltzmann equations for heavy neutrino as well as the light leptonic number densities to compute the final baryon asymmetry Y-B. Thus our analysis and results pertaining to a successful leptogenesis are more accurate than any other studies in existing literature that deal with perturbed TBM scenario. Finally, in the context of recent discovery of the ultra high energy (UHE) neutrino events at IceCube, assuming UHE neutrinos originate from purely astrophysical sources, we obtain prediction on the neutrino flux ratios at neutrino telescopes.