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

Abstract We obtain predictions for the Majorana phases α 21 / 2 and α 31 / 2 of the 3 × 3 unitary neutrino mixing matrix U = U e † U ν , U e and U ν 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 U e and U ν permitting to express α 21 / 2 and α 31 / 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 ξ 21 / 2 and ξ 31 / 2 present, in general, in U ν . The concrete forms of U ν considered are fixed by, or associated with, symmetries (tri-bimaximal, bimaximal, etc.), so that the angles in U ν are fixed. For each of these forms and forms of U e that allow to reproduce the measured values of the three neutrino mixing angles θ 12 , θ 23 and θ 13 , we derive predictions for phase differences ( α 21 / 2 − ξ 21 / 2 ) , ( α 31 / 2 − ξ 31 / 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 ξ 21 = 0 or π and ξ 31 = 0 or π . For these values of ξ 21 and ξ 31 and the best fit values of θ 12 , θ 23 and θ 13 , we present predictions for the effective Majorana mass in neutrinoless double beta decay for both neutrino mass spectra with normal and inverted ordering.