A general formalism is established for constructing models for the photoproduction of mesons from the nucleon. The essential ingredient is a mass operator which describes the coupling between meson-baryon, photon-baryon, and single-baryon channels. The most general forms for the mass operator interactions which produce these couplings are derived. These forms also provide generalizations of the Chew-Goldberger-Low-Nambu amplitudes for pion-nucleon photoproduction to any meson-baryon final state. The models lead to $S$-matrix elements that transform properly under inhomogeneous Lorentz transformations and are gauge invariant. The photoproduction amplitudes include final state interactions and satisfy Watson’s theorem. A specific model is constructed by deriving the mass operator interactions from effective Lagrangians that describe the couplings of mesons, photons, and baryons. The electromagnetic interactions include direct and crossed nucleon contributions, as well as direct contributions from the $P_{33}\left(1232\right)$, $P_{11}\left(1440\right)$, $D_{13}\left(1520\right)$, and $S_{11}\left(1535\right)$ resonances. A contact term and exchange terms due to the $\pi$, $\rho$, and $\omega$ mesons are also included. The model gives a good fit to the significant multipoles in the energy range from the single-pion, photoproduction threshold up to a center-of-momentum energy of $W=1550\text{MeV}$, which corresponds to a photon lab energy of $810\text{MeV}$.

• Received 15 August 2003

DOI:https://doi.org/10.1103/PhysRevC.68.064002