Predictions for the Majorana CP violation phases in the neutrino mixing matrix and neutrinoless double beta decay

We obtain predictions for the Majorana phases α21/2 and α31/2 of the 3×3 unitary neutrino mixing matrix U=Ue†Uν, Ue and Uν being the 3×3 unitary matrices resulting from the diagonalisation of the charged lepton and neutrino Majorana mass matrices, respectively. We focus on forms of Ue and Uν permitting to express α21/2 and α31/2 in terms of the Dirac phase δ and the three neutrino mixing angles of the standard parametrisation of U, and the angles and the two Majorana-like phases ξ21/2 and ξ31/2 present, in general, in Uν. The concrete forms of Uν considered are fixed by, or associated with, symmetries (tri-bimaximal, bimaximal, etc.), so that the angles in Uν are fixed. For each of these forms and forms of Ue that allow to reproduce the measured values of the three neutrino mixing angles θ12, θ23 and θ13, we derive predictions for phase differences (α21/2−ξ21/2), (α31/2−ξ31/2), etc., which are completely determined by the values of the mixing angles. We show that the requirement of generalised CP invariance of the neutrino Majorana mass term implies ξ21=0 or π and ξ31=0 or π. For these values of ξ21 and ξ31 and the best fit values of θ12, θ23 and θ13, we present predictions for the effective Majorana mass in neutrinoless double beta decay for both neutrino mass spectra with normal and inverted ordering.