CPV Predictions from Flavour Symmetries

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Pre-published on:
March 22, 2017

Published on:
June 20, 2017

Abstract

In the reference 3-neutrino mixing scheme leptonic CP violation can be caused by the Dirac, $\delta$, and/or Majorana, $\alpha_{21}$ and $\alpha_{31}$, CP-violating phases present in the unitary neutrino mixing matrix $U$. Using the fact that $U = U_e^\dagger U_\nu$, $U_e$ and $U_\nu$ being unitary matrices diagonalising the charged lepton and neutrino mass matrices, respectively, we consider in a systematic way forms of $U_e$ and $U_\nu$ allowing us to derive sum rules for $\cos\delta$, $\alpha_{21}$ and $\alpha_{31}$, i.e., to express them in terms of the measured neutrino mixing angles present in $U$ and the angles (and phases in the case of sum rules for $\alpha_{21}$ and $\alpha_{31}$) contained in $U_{\nu}$, whose values are fixed by a discrete flavour symmetry (a generalised CP symmetry). We consider several concrete forms of $U_\nu$, including the bimaximal, tri-bimaximal and golden ratio mixing forms. For each of these forms and forms of $U_e$ allowing to reproduce the measured values of the neutrino mixing angles, we obtain numerical predictions for $\delta$, $\alpha_{21}$ and $\alpha_{31}$. Using the obtained values of the CP-violating phases, we present predictions for the effective Majorana mass in neutrinoless double beta decay.

DOI: https://doi.org/10.22323/1.283.0027

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