U(1)_Q invariance and SU(3)_C X SU(3)_L X U(1)_X models with beta   arbitrary
  Using 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. 
Phung Van Dong and Hoang Ngoc Long