2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/206276Using the U(1)_Q invariance, the photon eigenstate and matching gauge coupling constants in SU(3)_C X SU(3)_L X U(1)_X models with beta arbitrary are given. The mass matrix of neutral gauge bosons is exactly diagonalized, and the photon eigenstate is independent on the symmetry breaking parameters - VEV's of Higgs scalars. By obtaining the electromagnetic vertex, the model is embedded naturally into the standard model.10 pagesHigh Energy Physics - Phenomenologytext