Nonzero $θ_{13}$, CP Violation, and $μ-τ$ Symmetry

The nonzero and relatively large $θ_{13}$ 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 $θ_{13}=0$. In order to accommodate nonzero $θ_{13}$ and CP violation, we modified TBM by introducing a simple perturbation matrix into TBM matrix that can produces $θ_{13}=7.89$ which is in agreement with the present experimental results. The Dirac phase $δ=77.20^{o}$ 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 $θ_{13}$ and $δ$ is the complex neutrino mass matrix. If we impose the $μ-τ$ 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 $μ-τ$ symmetry scheme.

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