U(1) Q invariance and ${SU}(3)_C\otimes SU(3)_{\mathrm {L}} \otimes {U}(1)_X$ models with $\beta$ arbitrary

Abstract

Using U(1)Q invariance, the photon eigenstate and the matching gauge coupling constants in \({SU}(3)_C\otimes {SU}(3)_{\mathrm {L}} \otimes {U}(1)_X\) models with arbitrary \(\beta\) are given. The mass matrix of the neutral gauge bosons is exactly diagonalized, and the photon eigenstate is independent on the symmetry breaking parameters - the VEVs of the Higgs scalars. By obtaining the electromagnetic vertex, the model is embedded naturally into the standard model.