Maximal CP-Violation in Neutrino Mass Matrix in light of the latest Daya Bay result on ${\theta }_{13}$

Abstract

The Daya Bay Collaboration (An et al) has recently proclaimed discovery of non-zero reactor angle, ${\theta }_{13}$, ${\sin }^{2}2{\theta }_{13}$=0.092$\pm$0.016(stat)$\pm$0.005(syst), at $5.2\sigma$ which is in conformity with the earlier observations of Abe et al, Adamson et al and Kerret et al last year. The discovery has immense implication for exploring CP-violation in the leptonic sector. In the present work, we examine CP-violation in Majorana neutrino mass matrix, in the basis where charged lepton mass matrix is diagonal, in which the ratio of elements are equal, also, termed as Strong Scaling Ans$\ddot{a}$tz (SSA). This Ans$\ddot{a}$tz has been known to explain the vanishing of ${\theta }_{13}$ and predict inverted hierarchy (IH) for the neutrino masses. However, to generate a non-zero value of ${\theta }_{13}$ consistent with Daya Bay result one has to deviate from SSA. This deviation will have important implications for CP-violation in the leptonic sector and is one of the issues addressed in the present work. CP is maximally violated because, for central value of ${\theta }_{13}$ obtained from Daya Bay experiment, Dirac-type phase $|\delta |\approx \frac{\pi }{2}$, $\frac{3\pi }{2}$ which corresponds to $|J_{CP}|\approx 0.03$. We have, also, studied imperative implications for Majorana-type phases $\alpha$, $\beta$ and effective neutrino mass, $M_{ee}$. The Majorana-type phases $\alpha$, $\beta$ are found to be sharply constrained.

Comments: 11 pages, 3 figures, references added