Perturbation to TBM mixing and its phenomenological implications

Abstract

To accommodate the recently observed non-zero reactor mixing angle ${\theta }_{13}$, we consider the lepton mixing matrix as Tri-bimaximal mixing (TBM) form in the leading order along with a perturbation in neutrino sector. The perturbation is taken to be a rotation in 23 plane followed by a rotation in 13 plane, i.e., $R_{23}({\theta }_{23}^{\prime })R_{13}({\theta }_{13}^{\prime },\varphi )$. We obtain the allowed values of the parameters ${\theta }_{23}^{\prime }$, ${\theta }_{13}^{\prime }$ and $\varphi$, which can accommodate all the observed mixing angles consistently and calculate the phenomenological observables such as the Dirac CP violating phase (${\delta }_{CP}$), Jarlskog invariant ($J_{CP}$), effective majorana mass $M_{ee}^{\nu }$, and $m_{{\nu }_e}$, the electron neutrino mass. We find that ${\delta }_{CP}$ can take any values between $0$ and $-\pi /2$ and $M_{ee}^{\nu }$ always comes below its experimental upper limit.

Comments: 13 pages, 3 figures