Majorana phase in minimal S3 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 S3 is assumed to be an exact flavor symmetry at the weak scale, is revisited. We find that S3 with an additional ZN symmetry allows one CP violating phase φν in the neutrino mixing. The leptonic sector contains six real parameters besides the phase φν to describe charged lepton and neutrino masses and the neutrino mixing. The model predicts: an inverted spectrum of neutrino mass, the absence of CP violating Dirac phase, tanθ23=1+O(me2/mμ2) and sinθ13=0.0034+O(memμ/mτ2). Neutrino mass as well as the effective Majorana mass 〈mee〉 in the neutrinoless double-β decay can be expressed in a closed form as a function of φν,Δm221,Δm223 and tanθ12. The model also predicts 〈mee〉⩾(0.036–0.066) eV.