Generalised CP and A4 family symmetry

Abstract

We perform a comprehensive study of family symmetry models based on A4 combined with the generalised CP symmetry H CP. We investigate the lepton mixing parameters which can be obtained from the original symmetry A4 ⋊ H CP breaking to different remnant symmetries in the neutrino and charged lepton sectors. We find that only one case is phenomenologically viable, namely $ G_{\mathrm{CP}}^{\nu}\cong Z_2^S\times H_{\mathrm{CP}}^{\nu } $ in the neutrino sector and $ G_{\mathrm{CP}}^l\cong Z_3^T\rtimes H_{\mathrm{CP}}^l $ in the charged lepton sector, leading to the prediction of no CP violation, namely δ CP and the Majorana phases α 21 and α 31 are all equal to either zero or π. We then propose an effective supersymmetric model based on the symmetry A4 ⋊ H CP in which trimaximal lepton mixing is predicted together with either zero CP violation or δ CP ≃ ±π/2 with non-trivial Majorana phases. An ultraviolet completion of the effective model yields a neutrino mass matrix which depends on only three real parameters. As a result of this, all three CP phases and the absolute neutrino mass scale are determined, the atmospheric mixing angle is maximal, and the Dirac CP can either be preserved with δ CP = 0, π or maximally broken with δ CP = ±π/2 and sharp predictions for the Majorana phases and neutrinoless double beta decay.