Nonzero ${\theta }_{13}$ and CP Violation from Broken $\mu -\tau$ Symmetry

Abstract

Nonzero and relatively large of ${\theta }_{13}$ mixing angle has some phenomenological consequences on neutrino physics beyond the standard model. One of the consequences if the mixing angle ${\theta }_{13}\ne 0$ is the possibility of the CP violation on the neutrino sector. In order to obtain nonzero ${\theta }_{13}$ mixing angle, we break the neutrino mass matrix that obey $\mu -\tau$ symmetry by introducing a complex parameter and determine the Jarlskog invariant as a measure of CP violation existence. By using the experimental data as input, we determine the Dirac phase $\delta$ as function of mixing angle ${\theta }_{13}$

Comments: 5 pages, no figure, abstract and section 3 extended