S3 x Z2 model for neutrino mass matrices

We propose a model for lepton mass matrices based on the seesaw mechanism, a complex scalar gauge singlet and a horizontal symmetry $S_3 \times \mathbbm{Z}_2$. In a suitable weak basis, the charged-lepton mass matrix and the neutrino Dirac mass matrix are diagonal, but the vacuum expectation value of the scalar gauge singlet renders the Majorana mass matrix of the right-handed neutrinos non-diagonal, thereby generating lepton mixing. When the symmetry $S_3$ is not broken in the scalar potential, the effective light-neutrino Majorana mass matrix enjoys $\mu$–$\tau$ interchange symmetry, thus predicting maximal atmospheric neutrino mixing together with $U_{e3}=0$. A partial and less predictive form of $\mu$–$\tau$ interchange symmetry is obtained when the symmetry $S_3$ is softly broken in the scalar potential. Enlarging the symmetry group $S_3\times \text{mathbbm}{Z}_2$ by an additional discrete electron-number symmetry $\text{mathbbm}{Z}_2^{(e)}$, a more predicitive model is obtained, which is in practice indistinguishable from a previous one based on the group $D_4$.