Neutrino mass matrix in a gauge group SU(2)L × U(1)e × U(1)μ × U(1)τ

Abstract

The electroweak unification group [Formula: see text] in which each fermion multiplet has its own [Formula: see text] factor was proposed in 1986 to get the neutrino mass matrix. In this paper, the gauge group [Formula: see text] is restricted to lepton section only, leaving quark multiplets as in the Standard Model. In addition to lepton multiplets [Formula: see text], [Formula: see text] and [Formula: see text], there are three [Formula: see text] singlet right-handed neutrinos [Formula: see text]’s. With the breaking of [Formula: see text] to [Formula: see text], the right-handed neutrinos acquire heavy Majorana masses. Three heavy right-handed neutrinos [Formula: see text]’s are available to generate a [Formula: see text] nondiagonal neutrino mass matrix in terms of three Yukawa couplings [Formula: see text], [Formula: see text], [Formula: see text] of the Higgs scalar doublet to [Formula: see text], [Formula: see text], [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text], respectively. Three Yukawa couplings can be arranged and expressed in terms of masses [Formula: see text], [Formula: see text], [Formula: see text] in three different ways to obtain the results of interest for Case 1: [Formula: see text]; Case 2: [Formula: see text]; Case 3: [Formula: see text]. The results obtained for the three cases are compared with the experimental data from neutrino oscillations. Cases 1 and 2 are relevant for solar neutrino oscillations whereas Case 3 is relevant for atmospheric neutrino oscillations.