Prediction of Neutrino Mixing based on $C_2\times D_3$

Abstract: The lepton mixing angles of the PMNS matrix are predicted based on the lepton flavor symmetry of a finite group $C_2\times D_3$, where the cyclic group $C_2$ acts on the charged lepton mass terms and the dihedral group $D_3$ on the neutrino ones. All three mixing angles of the PMNS matrix are given in terms of just one parameter, the charged lepton mixing angle, and fit extremely well to the observed values. In particular, the smallness of $\theta_{13}$ is explained in terms of the smallness of the muon-to-tau mass ratio.