GeneralizedCPandΔ(96)family symmetry

Abstract

We perform a comprehensive study of the $\mathrm{\ensuremath{\Delta}}(96)$ family symmetry combined with the generalized $CP$ symmetry ${H}_{CP}$. We investigate the lepton mixing parameters which can be obtained from the original symmetry $\mathrm{\ensuremath{\Delta}}(96)\ensuremath{\rtimes}{H}_{CP}$ breaking to different remnant symmetries in the neutrino and charged lepton sectors, namely ${G}_{\ensuremath{\nu}}$ and ${G}_{l}$ subgroups in the neutrino and the charged lepton sector, respectively, and the remnant $CP$ symmetries from the breaking of ${H}_{CP}$ are ${H}_{CP}^{\ensuremath{\nu}}$ and ${H}_{CP}^{l}$, respectively, where all cases correspond to a preserved symmetry smaller than the full Klein symmetry, as in the semidirect 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 ${\ensuremath{\chi}}^{2}$ determination of the best fit parameters and the correlations between mixing parameters, in each case.