Perturbation to TBM mixing and its phenomenological implications

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., $R_{23}(\theta_{23}')R_{13}(\theta_{13}',\phi)$. We obtain the allowed values of the parameters $\theta_{23}'$, $\theta_{13}'$ and $\phi$, 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.