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Predictions for the Majorana CP Violation Phases in the Neutrino Mixing Matrix and Neutrinoless Double Beta Decay

We obtain predictions for the Majorana phases $α_{21}/2$ and $α_{31}/2$ of the $3\times 3$ unitary neutrino mixing matrix $U = U_e^{\dagger} \, U_ν$, $U_e$ and $U_ν$ being the $3\times 3$ 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.