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

Abstract

If we impose the $\mu -\tau$ symmetry, as a constraint into neutrino mass matrix, one find that the Jarlskog rephasing invariant: $J_{\mathrm{CP}}=0$ which implies that CP violation cannot be accommodated in the $\mu -\tau$ symmetry scheme. By introducing a small parameter $x$ that perturb the neutrino mass matrix with $\mu -\tau$ symmetry with trace of neutrino mass matrix remain constant, we can obtain $J_{CP}\ne 0$ and consequently ${\theta }_{13}\ne 0$.

Comments: 3 references added, Talk given at 16th Lomonosov Conference on Elementary Particle Physics, Moscow, 22-28 August 2013