Nonzero |U_e3| from Charged Lepton Corrections and the Atmospheric Neutrino Mixing Angle

Abstract

After the successful determination of the reactor neutrino mixing angle θ_13 ~ 0.16 \neq 0, a new feature suggested by the current neutrino oscillation data is a sizeable deviation of the atmospheric neutrino mixing angle θ_23 from π/4. Using the fact that the neutrino mixing matrix U = U_e^\dagger U_ν, where U_e and U_νresult from the diagonalisation of the charged lepton and neutrino mass matrices, and assuming that U_νhas a i) bimaximal (BM), ii) tri-bimaximal (TBM) form, or else iii) corresponds to the conservation of the lepton charge L' = L_e - L_μ- L_τ(LC), we investigate quantitatively what are the minimal forms of U_e, in terms of angles and phases it contains, that can provide the requisite corrections to U_νso that θ_13, θ_23 and the solar neutrino mixing angle θ_12 have values compatible with the current data. Two possible orderings of the 12 and the 23 rotations in U_e, "standard" and "inverse", are considered. The results we obtain depend strongly on the type of ordering. In the case of "standard" ordering, in particular, the Dirac CP violation phase δ, present in U, is predicted to have a value in a narrow interval around i) δ~ πin the BM (or LC) case, ii) δ~ 3π/2 or π/2 in the TBM case, the CP conserving values δ= 0, π, 2πbeing excluded in the TBM case at more than 4σ. In the addendum we discuss the implications of the latest 2013 data.