Fermion mass hierarchies and flavour mixing from a minimal discrete symmetry

We construct a simple model of fermion masses based on a spontaneously broken S3×Z3S3×Z3 flavour group. At the leading order, in the neutrino sector S3S3 is broken down to a νμ–ντνμ–ντ parity subgroup that enforces a maximal atmospheric mixing angle and a vanishing θ13θ13. In the charged lepton sector the νμ–ντνμ–ντ parity is maximally broken and the resulting mass matrix is nearly diagonal. The charged lepton mass hierarchy is automatically reproduced by the S3S3 symmetry breaking parameter alone. A careful analysis shows that, after the inclusion of all relevant subleading effects, the model predicts θ23=π/4+O(λc2) and θ13=O(λc2), λcλc denoting the Cabibbo angle. A simple extension to the quark sector is also illustrated, where the mass spectrum and the mixing angles are naturally reproduced, with the exception of the mixing angle between the first two generations, that requires a small accidental enhancement.