Pion photoproduction on nucleons in a covariant hadron-exchange model

We present a relativistic dynamical model of pion photoproduction on the nucleon in the resonance region. It offers several advances over the existing approaches. The model is obtained by extending our $\pi N$-scattering description to the electromagnetic channels. The resulting photopion amplitude is thus unitary in the $\pi N$, $\text{ga}N$ channel space, Watson’s theorem is exactly satisfied. At this stage we have included the pion, nucleon, $\text{De}(1232)$-resonance degrees of freedom. The $\rho$ and $\omega$ meson exchanges are also included, but play a minor role in the considered energy domain (up to $\sqrt{s}=1.5$ GeV). In this energy range the model provides a good description of all the important multipoles. We have allowed for only two free parameters – the photocouplings of the $\mathrm{\Delta }$-resonance. These couplings are adjusted to reproduce the strength of corresponding resonant-multipoles $M_{1+}$ and $E_{1+}$ at the resonance position.