Neutrino mass matrix from S4 symmetry

The cubic symmetry S4 contains A4 and S3, both of which have been used to study neutrino mass matrices. Using S4 as the family symmetry of a complete supersymmetric theory of leptons, it is shown how the requirement of breaking S4 at the seesaw scale without breaking supersymmetry enforces a special form of the neutrino mass matrix which exhibits maximal νμ-ντ mixing as well as zero Ue3. In addition, (νe+νμ+ντ)/3 is naturally close to being a mass eigenstate, thus predicting tan2θ12 to be near but not equal to 1/2.