Neutrino Oscillation and S4 Flavor Symmetry

Observations of neutrino oscillations are very strong evidence for the existence of neutrino masses and mixing. From recent experimental results on neutrino oscillation, we find that neutrino mixing angles are quite consistent with the so-called tri-bi-maximal mixing pattern, but the deviation from observational results is non-negligible. However, the tri-bi-maximal mixing pattern is still useful as a leading order approximation and provides a good guideline to search for the flavor symmetry in the neutrino sector. We introduce the $S_4$ permutation symmetry as a flavor symmetry to the standard model of particle physics with additional particle contents of heavy right-handed neutrinos and scalar fields. Finally, we obtain the tri-bi-maximal mixing pattern as a mixing matrix in the lepton sector within the suggested model. To derive the required unitary mixing matrix for the neutrino sector, the double seesaw mechanism is utilized.