Nonzero $\theta_{13}$ and CP violation from Broken $\mu-\tau$ Symmetry with $m_{1}=0$

TL;DR

This paper explores how breaking mu-tau symmetry in the neutrino mass matrix can generate a nonzero mixing angle θ13 and CP violation, using a small perturbation and experimental data with m1=0.

Contribution

It introduces a method to break mu-tau symmetry with a small parameter to produce nonzero θ13 and analyze CP violation in neutrino physics.

Findings

Nonzero θ13 can be achieved by breaking mu-tau symmetry.

CP violation is possible with the introduced symmetry breaking.

Results are consistent with experimental data.

Abstract

Nonzero of mixing angle $\theta_{13}$ has some phenomenological consequences on neutrino physics beyond the standard model. If the mixing angle $\theta_{13}\neq 0$, then there is the possibility of the CP violation existence on the neutrino sector. To obtain a nonzero of mixing angle $\theta_{13}$ from neutrino mass matrix obey $\mu-\tau$, we break it by introducing one small parameter $x$ into neutrino mass matrix and then calculated the Jarlskog invariant as a measure of CP violation existence using the reported experimental data as input and put $m_{1}=0$ for neutrino mass in normal hierarchy.