Non-vanishing U e3 under S 3 symmetry

This work proposes two models of neutrino masses that predict non-zero θ13 under the non-Abelian discrete flavor symmetry \(\mathbb{S}_{3}\otimes\mathbb{Z}_{2}\). We advocate that the size of θ13 is understood as a group theoretical consequence rather than a perturbed effect from the tri-bi-maximal mixing. So, the difference of two models is designed only in terms of the flavor symmetry, by changing the charge assignment of right-handed neutrinos. The PMNS matrix in the first model is obtained from both mass matrices, charged leptons giving rise to non-zero \(\theta^{l}_{13}\) and neutrino masses giving rise to tri-bi-maximal mixing. The physical mixing angles are expressed by a simple relation between \(\theta^{l}_{13}\) and tri-bi-maximal angles to fit the recent experimental results. The other model generates PMNS matrix with non-zero θ13, only from the neutrino mass transformation. The 5-dimensional effective theory of Majorana neutrinos obtained in this framework is tested with phenomenological bounds in the parametric spaces sinθ23,sinθ12 and m2/m3 vs. sinθ13.