U(1)_Q invariance and SU(3)_C X SU(3)_L X U(1)_X models with beta arbitrary

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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.
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