Predicting the values of the leptonic CP violation phases in theories with discrete flavour symmetries

摘要

Using the fact that the neutrino mixing matrix U = (UeU nu)-U-dagger, where U-e and U-nu result from the diagonalisation of the charged lepton and neutrino mass matrices, we consider a number of forms of U-nu associated with a variety of discrete symmetries: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding iii) to the conservation of the lepton charge L' = L-e - L-mu - L-tau (LC), iv) to golden ratio type A (GRA) mixing, v) to golden ratio type B (GRB) mixing, and vi) to hexagonal (HG) mixing. Employing the minimal form of U-e, in terms of angles and phases it contains, that can provide the requisite corrections to U-nu so that reactor, atmospheric and solar neutrino mixing angles theta(13), theta(23) and theta(12) have values compatible with the current data, including a possible sizable deviation of theta(23) from pi/4, we discuss the possibility to obtain predictions for the CP violation phases in the neutrino mixing matrix. Considering the "standard ordering" of the 12 and the 23 rotations in U-e and following the approach developed in [1] we derive predictions for the Dirac phase delta and the rephasing invariant J(CP) in the cases of GRA, ORB and HG forms of U-nu (results for the TBM and BM (LC) forms were obtained in [1]). We show also that under rather general conditions within the scheme considered the values of the Majorana phases in the PMNS matrix can be predicted for each of the forms of U-nu discussed. We give examples of these predictions and of their implications for neutrinoless double beta decay. In the GRA, ORB and HG cases, as in the TBM one, relatively large CP violation effects in neutrino oscillations are predicted (vertical bar J(CP)vertical bar similar to (0.031-0.034)). Distinguishing between the TBM, BM (LC), GRA, GRB and HG forms of U-nu requires a measurement of cos (3 or a relatively high precision measurement of J(CP).