Lepton Mixing Parameters from $\Delta(48)$ Family Symmetry and Generalised CP

Abstract

We provide a systematic and thorough exploration of the $\Delta(48)$ family symmetry and the consistent generalised CP symmetry. A model-independent analysis of the achievable lepton flavor mixing is performed by considering all the possible remnant symmetries in the neutrino and the charged lepton sectors. We find a new interesting mixing pattern in which both lepton mixing angles and CP phases are nontrivial functions of a single parameter $\theta$. The value of $\theta$ can be fixed by the measured reactor mixing angle $\theta_{13}$, and the excellent agreement with the present data can be achieved. A supersymmetric model based on $\Delta(48)$ family symmetry and generalised CP symmetry is constructed, and this new mixing pattern is exactly reproduced.