  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 $S_3 \times \mathbbm{Z}_2$ by an additional
discrete electron-number symmetry $\mathbbm{Z}_2^{(e)}$, a more predicitive
model is obtained, which is in practice indistinguishable from a previous one
based on the group $D_4$.

High Energy Physics - Phenomenology