Majorana Phase in Minimal S_3 Invariant Extension of the Standard Model

Abstract

The leptonic sector in a recently proposed minimal extension of the standard model, in which the permutation symmetry S_3 is assumed to be an exact flavor symmetry at the weak scale, is revisited. We find that S_3 with an additional Z_{N} symmetry allows CP violating phases in the neutrino mixing. The leptonic sector contains six real parameters with two independent phases to describe charged lepton and neutrino masses and the neutrino mixing. The model predicts: an inverted spectrum of neutrino mass, tan theta_{23}=1+O(m_e^2/m_mu^2) and sin theta_{13}=m_e/sqrt{2}m_mu+O(m_em_mu/m_{tau}^2) simeq 0.0034. Neutrino mass as well as the effective Majorana mass in the neutrinoless double-beta decay can be expressed in a closed form as a function of phi_nu, Delta m^2_{21},Delta m^2_{23} and tantheta_{12}, where phi_nu is one of the independent phases. The model also predicts geq (0.036 - 0.066) eV.