1305.0248 (Takeshi Araki)

Is θ_{13}^{PMNS} correlated with θ_{23}^{PMNS} or not?    [PDF]

Takeshi Araki

By assuming the Tri-Bi-Maximal mixing at leading order and postulating \theta_{23} \simeq 45^\circ + \eta\theta_{13} where \eta is equal to \pm 1/\sqrt{2} or 0, we seek for preferable correction terms to the charged lepton and neutrino mass matrices and discuss their origins. The global fits of neutrino oscillation parameters favor the case of \eta=\pm 1/\sqrt{2}; it corresponds to the relation found by Edy, Frampton and Mastuzaki some years ago in the context of a T^\prime flavor model. In contrast, the results from the \nu_\mu disappearance mode reported by the T2K and Super-Kamiokande collaborations prefer \eta=0, which results in the almost maximal \theta_{23}. We derive a general condition for obtaining \theta_{23} \simeq 45^\circ + \eta\theta_{13}. The condition is complicated by the neutrino masses and CP violating phases, so that we simplify the condition by supposing vanishing Majorana phases, the quasi-degenerate neutrino masses, etc.. Under such simplified environments, we find out several correction terms that take very simple forms. It is also shown that the obtained correction terms indeed arise from the spontaneous breaking of a flavor symmetry or one-loop radiative corrections.

View original: http://arxiv.org/abs/1305.0248