Generalised CP and $Δ(96)$ Family Symmetry

We perform a comprehensive study of the $Δ(96)$ family symmetry combined with the generalised CP symmetry $H_{\rm{CP}}$. We investigate the lepton mixing parameters which can be obtained from the original symmetry $Δ(96)\rtimes H_{\rm{CP}}$ breaking to different remnant symmetries in the neutrino and charged lepton sectors, namely $G_ν$ and $G_l$ subgroups in the neutrino and the charged lepton sector respectively, and the remnant CP symmetries from the breaking of $H_{\rm{CP}}$ are $H^ν_{\rm{CP}}$ and $H^{l}_{\rm{CP}}$, 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 $χ^2$ determination of the best fit parameters and the correlations between mixing parameters, in each case.

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