Unifying the electroweak and B − L interactions

We argue that the gauge symmetry which includes SU(3)L as a higher weak-isospin symmetry is manifestly given by SU(3)C[+ in circle]SU(3)L[+ in circle]U(1)X[+ in circle]U(1)N, where the last two factors determine the electric charge and B-L, respectively. This theory not only provides a consistent unification of the electroweak and B-L interactions, but also gives insights in dark matter, neutrino masses, and inflation. The dark matter belongs to a class of new particles that have wrong B-L numbers, and is stabilized due to a newly realized W-parity as residual gauge symmetry. The B-L breaking field is important to define the W-parity, seesaw scales, and the inflaton. Furthermore, the number of fermion generations and the electric charge quantization are explained naturally. We also show that the previous 3-3-1 models are only an effective theory, as the B-L charge and the unitarity argument are violated. This work substantially generalizes our recently proposed 3-3-1-1 model.