Predicting the Values of the Leptonic CP Violation Phases

Abstract

Using the fact that the neutrino mixing matrix $U=U_e^{†}{U}_{\nu }$, 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 flavour symmetries: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding iii) to the conservation of the lepton charge $L^{\prime }=L_e-L_{\mu }-L_{\tau }$ (LC), iv) to golden ratio type A (GRA) mixing, v) golden ratio type B (GRB) mixing, and iii) to hexagonal (HG) mixing. Employing the minimal form of $U_e$ 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. Following the approach developed in [1] we derive predictions for the Dirac phase $\delta$ and the rephasing invariant $J_{\mathrm{CP}}$ in the cases of GRA, GRB 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, GRB and HG cases, as in the TBM one, relatively large CP violation effects in neutrino oscillations are predicted ($|J_{CP}|\sim (0.031-0.034)$). Distinguishing between the TBM, BM (LC), GRA, GRB and HG forms of $U_{\nu }$ requires a measurement of $\cos \delta$ or a relatively high precision measurement of $J_{\mathrm{CP}}$.

Comments: 30 pages, results unchanged, title modified, text (including the Introduction) streamlined, with exception of a few added references version to be published in Nuclear Physics B