Neutrino Mixing and Leptonic CP Violation from $S_4$ Flavour and Generalised CP Symmetries

Abstract

We consider a class of models of neutrino mixing with $S_4$ lepton flavour symmetry combined with a generalised CP symmetry, which are broken to residual $Z_2$ and $Z_2\times H_{\mathrm{CP}}^{\nu }$ symmetries in the charged lepton and neutrino sectors, respectively, $H_{\mathrm{CP}}^{\nu }$ being a remnant CP symmetry of the neutrino Majorana mass term. In this set-up the neutrino mixing angles and CP violation (CPV) phases of the neutrino mixing matrix depend on three real parameters - two angles and a phase. We classify all phenomenologically viable mixing patterns and derive predictions for the Dirac and Majorana CPV phases. Further, we use the results obtained on the neutrino mixing angles and leptonic CPV phases to derive predictions for the effective Majorana mass in neutrinoless double beta decay.

Comments: 56 pages, includes 16 figures and 8 tables; the discussion on the possibility to discriminate experimentally between the different cases extended and a new related figure added; the discussion of neutrinoless double beta decay extended; references added; typos corrected; matches version published in JHEP