Electromagnetic interaction in chiral quantum hadrodynamics and decay of vector and axial-vector mesons

The chiral invariant quantum hadrodynamics (QHD) III model of Serot and Walecka is applied in the calculation of some meson properties. The electromagnetic interaction is included by extending the symmetry of the model to the local $\mathrm{U}\mathrm{}\left(1\right)\mathrm{}\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L$ group. The minimal and nonminimal contributions to the electromagnetic Lagrangian are obtained in a new representation of QHD-III. Strong decays of the axial-vector meson, $a_1\to \pi \rho ,a_1\to \pi \sigma ,$ and the electromagnetic decays $\overrightarrow{\rho }\pi \pi \gamma ,a_1\to \pi \gamma ,$ and $\overrightarrow{\rho }\pi \gamma$ are calculated. The low-energy parameters for the $\pi -\pi$ scattering are calculated in the tree-level approximation. The effect of the auxiliary Higgs bosons, introduced in QHD-III in order to generate masses of the vector and axial-vector mesons via the Higgs mechanism, is studied as well. This is done on the tree level for $\pi -\pi$ scattering and on the level of one-loop diagrams for the $a_1\to \pi \gamma$ decay. It is demonstrated that the model successfully describes some features of meson phenomenology in the nonstrange sector.