Predictions for the Dirac Phase in the Neutrino Mixing Matrix and Sum Rules

Using the fact that the neutrino mixing matrix U = U^†_eU_ν, where U_e and U_v 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 U_v has a form dictated by, or associated with, discrete symmetries and U_e has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to U_v, so that reactor, atmospheric and solar neutrino mixing angles θ₁₃, θ₂₃ and θ₁₂ 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' = L_e — L_μ — L_τ (LC)), iii) golden ratio type A (GRA), iv) golden ratio type B (GRB), and v) hexagonal (HG). We investigate the predictions for 5 in the cases of TBM, BM (LC), GRA, GRB and HG forms using the exact and the leading order sum rules for cos δ proposed in the literature, taking into account also the uncertainties in the measured values of sin² θ₁₂, sin² θ₂₃ and sin² θ₁₃. This allows us, in particular, to assess the accuracy of the predictions for cos 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. (paper)