Multipole analysis of pion photoproduction based on fixed t dispersion relations and unitarity

We have analyzed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipoles were derived from the dispersion relations and solved by the method of Omnès and Muskhelishvili. The free parameters were determined by a fit to the most recent data for π⁺ and π⁰ production on the proton as well as π⁻ production on the neutron, in the energy range 160 MeV ⩽ E_γ ⩽ 420 MeV. The lack of high precision data on the neutron and of polarization observables leads to some limitations of our results. Especially the multipole M₁₋ connected with the Roper resonance P₁₁ (1440) cannot be determined to the required precision. Our predictions for the threshold amplitudes are in good agreement with both the data and chiral perturbation theory. In the region of the Δ(1232) we have determined the ratio of electric quadrupole and magnetic dipole excitation. The position of the resonance pole is obtained in exellent agreement with pion-nucleon scattering, and the complex residues of the multipoles are determined with the speed-plot technique.