Nonzero $\theta_{13}$, CP Violation, and $\mu-\tau$ Symmetry

The nonzero and relatively large $\theta_{13}$ from the latest experimental results have a serious implication on the well-known neutrino mixing matrix. One of the well-known mixing matrix is tribimaximal (TBM) neutrino mixing matrix which predict $\theta_{13}=0$. In order to accommodate nonzero $\theta_{13}$ and CP violation, we modified TBM by introducing a simple perturbation matrix into TBM matrix that can produces $\theta_{13}=7.89$ which is in agreement with the present experimental results. The Dirac phase $\delta=77.20^{o}$ and the Jarlskog rephasing invariant: $J_{\rm CP}\approx 0.044$ are also obtained. The obtained neutrino mass matrix from the modified TBM with both nonzero $\theta_{13}$ and $\delta$ is the complex neutrino mass matrix. If we impose the $\mu-\tau$ symmetry, as a constraint into neutrino mass matrix,one find that the Jarlskog rephasing invariant: $J_{\rm CP}=0$ which implies that CP violation cannot be accommodated in the $\mu-\tau$ symmetry scheme.