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

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. By introducing a small parameter $x$ that perturb the neutrino mass matrix with $μ-τ$ symmetry with trace of neutrino mass matrix remain constant, we can obtain $J_{CP}\neq 0$ and consequently $θ_{13}\neq 0$.

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