Is θ₁₃PMNS correlated with θ₂₃PMNS or not?

Original · EN

By postulating the relation θ₂₃ ≃ 45∘ + ηθ₁₃, we seek preferable correction terms to tri-bi-maximal mixing and discuss their origins. Global analyses of the neutrino oscillation parameters favor η=± 1/√2; this corresponds to the relation found by Edy, Frampton, and Matsuzaki some years ago in the context of a T′ flavor symmetry. In contrast, the results of the νμdisappearance mode reported by the T2K and Super-Kamiokande collaborations seem to prefer η=0, which gives an almost maximal θ₂₃. We derive a general condition for ensuring θ₂₃ ≃ 45∘ + ηθ₁₃ and find that the condition is complicated by the neutrino masses and CP violating phases. We investigate the condition under simplified environments and arrive at several correction terms to the mass matrices. It is found that the obtained correction terms can arise from flavor symmetries or one-loop radiative corrections.