Eur. Phys. J. C (2012) 72: 2081
https://doi.org/10.1140/epjc/s10052-012-2081-3

Regular Article - Theoretical Physics

Non-vanishing U _e3 under S ₃ symmetry

Department of Physics, Chung-Ang University, Seoul, 156-756, South Korea

^* e-mail: siyeon@cau.ac.kr

Received: 19 May 2012
Revised: 4 July 2012
Published online: 18 July 2012

Abstract

This work proposes two models of neutrino masses that predict non-zero θ ₁₃ under the non-Abelian discrete flavor symmetry . We advocate that the size of θ ₁₃ 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 and neutrino masses giving rise to tri-bi-maximal mixing. The physical mixing angles are expressed by a simple relation between and tri-bi-maximal angles to fit the recent experimental results. The other model generates PMNS matrix with non-zero θ ₁₃, 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 sinθ ₂₃,sinθ ₁₂ and m ₂/m ₃ vs. sinθ ₁₃.