Relatively large θ13 and nearly maximal θ23 from the approximate S3 symmetry of lepton mass matrices

We apply the permutation symmetry S3 to both charged-lepton and neutrino mass matrices, and suggest a useful symmetry-breaking scheme, in which the flavor symmetry is explicitly broken down via S3→Z3→∅ in the charged-lepton sector and via S3→Z2→∅ in the neutrino sector. Such a two-stage breaking scenario is reasonable in the sense that both Z3 and Z2 are the subgroups of S3, while Z3 and Z2 only have a trivial subgroup. In this scenario, we can obtain a relatively large value of the smallest neutrino mixing angle, e.g., θ13≈9°, which is compatible with the recent result from T2K experiment and will be precisely measured in the ongoing Double Chooz and Daya Bay reactor neutrino experiments. Moreover, the maximal atmospheric mixing angle θ23≈45° can also be obtained while the best-fit value of solar mixing angle θ12≈34° is assumed, which cannot be achieved in previous S3 symmetry models.