Determining the Dirac CP violation phase in the neutrino mixing matrix from sum rules

Using the fact that the neutrino mixing matrix U=Ue†Uν, where UeUe and UνUν result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the sum rules which the Dirac phase δ present in U   satisfies when UνUν has a form dictated by, or associated with, discrete symmetries and UeUe has a “minimal” form (in terms of angles and phases it contains) that can provide the requisite corrections to UνUν, so that reactor, atmospheric and solar neutrino mixing angles θ13θ13, θ23θ23 and θ12θ12 have values compatible with the current data. The following symmetry forms are considered: i) tri-bimaximal (TBM), ii) bimaximal (BM) (or corresponding to the conservation of the lepton charge L′=Le−Lμ−LτL′=Le−Lμ−Lτ (LC)), iii) golden ratio type A (GRA), iv) golden ratio type B (GRB), and v) hexagonal (HG). We investigate the predictions for δ   in the cases of TBM, BM (LC), GRA, GRB and HG forms using the exact and the leading order sum rules for cos⁡δcos⁡δ proposed in the literature, taking into account also the uncertainties in the measured values of sin2⁡θ12sin2⁡θ12, sin2⁡θ23sin2⁡θ23 and sin2⁡θ13sin2⁡θ13. This allows us, in particular, to assess the accuracy of the predictions for cos⁡δcos⁡δ based on the leading order sum rules and its dependence on the values of the indicated neutrino mixing parameters when the latter are varied in their respective 3σ experimentally allowed ranges.