Nonzero θ_(13), CP Violation, and Broken μ - τ Symmetry

摘要

Recently, evidence for a nonzero and relatively large θ_(13), as measured in the latest experiment, has a strong implication on the well-known neutrino mixing matrix and the existence of CP violation in the neutrino sector (J_(CP) ≠ 0). One of the well-known mixing matricies is the tribimaximal (TBM) neutrino mixing matrix that predicts the mixing angle θ_(13) = 0 and J_(CP) = 0. In order to accommodate a nonzero θ_(13) and CP violation, we modified the TBM by introducing a simple perturbation matrix into the TBM matrix that can produce θ_(13) = 7.89°, which is in agreement with the current experimental results, and the Dirac phase δ ≈ π/2 and J_(CP) ≈ 0.0222. The obtained neutrino mass matrix from the modified TBM with both nonzero θ_(13) and δ is a complex neutrino mass matrix. If we impose μ - τ symmetry as a constraint into the neutrino mass matrix, one finds that the J_(CP) = 0, which implies that CP violation cannot be accommodated in the μ - τ symmetry scheme. We break the μ - τ symmetry softly by introducing a small parameter x to perturb the neutrino mass matrix with the constraint that the trace of the perturbed neutrino mass matrix remains constant.