Seesaw neutrino mass and new U(1)U(1) gauge symmetry

The three electroweak doublet neutrinos νe,μ,τνe,μ,τ of the Standard Model may acquire small seesaw masses, using either three Majorana fermion singlets N   or three Majorana fermion triplets (Σ+,Σ0,Σ−)(Σ+,Σ0,Σ−). It is well known that the former accommodates the U(1)U(1) gauge symmetry B−LB−L. It has also been shown some years ago that the latter supports a new U(1)XU(1)X gauge symmetry. Here we study two variations of this U(1)XU(1)X, one for two N and one Σ, the other for one N and two Σ. Phenomenological consequences are discussed.