Unitary, gauge invariant, relativistic resonance model for pion photoproduction

Pion photoproduction up to 770 MeV photon laboratory energy is described by a manifestly covariant wave equation, which includes a treatment of the final state πN interactions consistent with the covariant, unitary, resonance model of πN scattering previously developed. The kernel of the equation includes nucleon (N), Roper (${\mathit{N}}^{\mathrm{*}}$), delta (Δ), and ${\mathit{D}}_{13}$ poles and their crossed poles, as well as π, ρ, and ω exchange terms. The Kroll-Rudermann term and other interaction currents ensure that the model is exactly gauge invariant to all orders in the strong coupling ${\mathit{g}}_{\mathrm{\pi }\mathit{NN}}$. The threshold value of the ${\mathit{E}}_{0+}$ amplitude is in good agreement with recent estimates obtained from chiral perturbation theory. Elastic unitarity to first order in the charge e (Watson theorem) is maintained up to the two-pion production threshold. The complete development of this model, which gives a good fit to all L≤2 multiples up to 770 MeV, is presented. © 1996 The American Physical Society.