Predicting the leptonic Dirac CP violation phase from sum rules

Establishing the status of the CP symmetry in the lepton sector is one of the major goals of the programme of future research in neutrino physics. In the reference 3-neutrino mixing scheme CP-violating effects in neutrino oscillations can be caused by the Dirac CP violation phase δ present in the 3 × 3 unitary neutrino mixing matrix U . Using the fact that U = Ue†Uν , where Ue and Uν are 3 × 3 unitary matrices which diagonalise respectively the charged lepton and neutrino mass matrices, we consider in a systematic way forms of Ue and Uν allowing us to express δ as a function of the neutrino mixing angles present in U and the angles contained in Uν . After obtaining sum rules for cos δ , we consider several forms of Uν dictated by, or associated with, symmetries, such as tri-bimaximal, bimaximal, etc., for which the angles in Uν are fixed. For each of these forms and forms of Ue allowing to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for cosδ, using the prospective uncertainties in the determination of the neutrino mixing angles. Our results show that the measurement of δ along with improvement of the precision on the neutrino mixing angles can provide unique information as regards the possible existence of symmetry in the lepton sector.