Generalised CP and $\Delta (96)$ Family Symmetry

Abstract

We perform a comprehensive study of the $\Delta (96)$ family symmetry combined with the generalised CP symmetry $H_{\mathrm{CP}}$. We investigate the lepton mixing parameters which can be obtained from the original symmetry $\Delta (96)⋊H_{\mathrm{CP}}$ breaking to different remnant symmetries in the neutrino and charged lepton sectors, namely $G_{\nu }$ and $G_l$ subgroups in the neutrino and the charged lepton sector respectively, and the remnant CP symmetries from the breaking of $H_{\mathrm{CP}}$ are $H_{\mathrm{CP}}^{\nu }$ and $H_{\mathrm{CP}}^l$, respectively, where all cases correspond to a preserved symmetry smaller than the full Klein symmetry, as in the semi-direct approach, leading to predictions which depend on a single undetermined real parameter, which may be fitted to the reactor angle for example. We discuss 26 possible cases, including a global ${\chi }^2$ determination of the best fit parameters and the correlations between mixing parameters, in each case.

Comments: 71 pages, 10 figures