Abstract
The possibility of a model with a massive fermion, axial-vector and scalar mesons, and a massless vector meson originating as a dynamical consequence of a chiral U(1) \ifmmode\times\else\texttimes\fi{} U(1) gauge-invariant model with a massless fermion and vector and axial-vector mesons is explored. A recent approach due to Cornwall which makes use of an effective Lagrangian combined with the Callan-Symanzik equations, and its extension, are used with an assumption similar to that of the Baker-Johnson finite quantum electrodynamics. The physical quartic scalar coupling constant and the ratios of physical masses of axial-vector and scalar mesons with respect to that of fermions are expressed in terms of the vector and axial-vector gauge coupling constants.
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