CP transformed mixed $\mu \tau$ antisymmetry for neutrinos and its consequences

Abstract

We propose a complex extension of mixed $\mu \tau$ antisymmetry in the neutrino Majorana mass matrix $M_{\nu }$. This can be implemented in the Lagrangian by a generalized CP transformation (labeled by a mixing parameter $\theta$) on the left-chiral flavor neutrino fields. We investigate its implications for leptonic CP violation and neutrino phenomenology in general. Interestingly, the $\mu \tau$ mixing parameter $\theta$ gets correlated with the Dirac CP phase $\delta$ and the atmospheric mixing angle ${\theta }_{23}$ through an analytical relation. In general, for arbitrary $\theta$, both ${\theta }_{23}$ and $\delta$ are nonmaximal. We discuss the corresponding results for the CP asymmetry parameter $A_{\mu e}$ in neutrino oscillation experiments. For a nonmaximal $\delta$, one of the two Majorana phases is different from $0$ or $\pi$, thereby leading to nonvanishing Majorana CP violation with observable consequences for the neutrinoless double beta ($\beta \beta 0\nu$) decay process. We numerically work out in detail the predictions for that process in relation to various ongoing and forthcoming experiments. We also work out the predictions of our scheme on flavor flux ratios at neutrino telescopes. While exact CP transformed $\mu \tau$ interchange antisymmetry ($\theta =\pi /2$) leads to an exact equality among those ratios, taking a value $0.5$, a tiny deviation can cause a drastic change in them. Careful measurement of these flux ratios in future will further constrain the parameter $\theta$.

Comments: 20 pages, 28 figures. A few extra sentences have been added in Section 1 pointing out the realization of a class of symmetries discussed here in high scale models within a unified discrete flavor symmetry group. Some additional references have also been inserted