A new operator for pion photo-and electroproduction has been developed for nuclear applications at photon equivalent energies up to 1 GeV. The model contains Born terms, vector mesons and nucleon resonances (P33(1232), P11(1440), D13(1520), S11(1535), F15(1680), and D33 (1700)). The resonance contributions are included taking into account unitarity to provide the correct phases of the pion photoproduction multipoles. The Q 2 dependence of electromagnetic resonance vertices is described with appropriate form factors in the electromagnetic helicity amplitudes. Within this model we have obtained good agreement with the experimental data for pion photo-and electroproduction on the nucleon for both differential cross sections and polarization observables. The model can be used as a starting point to predict and analyze forthcoming data.

We h a v e analysed pion photoproduction imposing constraints from xed t dispersion relations and unitarity. Coupled integral equations for the S and P wave m ultipoles were derived from the dispersion relations and solved by the method of Omnes and Muskhelishvili. The free parameters were determined by a t to the most recent data for + and 0 production on the proton as well as production on the neutron, in the energy range 160 MeV E 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 (1232) we h a v e determined the ratio of electric quadrupole and magnetic dipole excitation. The position of the resonance pole is obtained in excellent agreement with pion-nucleon scattering, and the complex residues of the multipoles are determined with the speed-plot technique.

Recent JLab data of the differential cross section for the reaction p(e, e ′ p)π 0 in the invariant mass region of 1.1 < W < 1.4 GeV at four-momentum transfer squared Q 2 = 2.8 and 4.0 (GeV/c) 2 are analyzed with two models, both of which give an excellent description of most of the existing pion electroproduction data below W < 1.5 GeV. We find that at up to Q 2 = 4.0(GeV/c) 2 , the extracted helicity amplitudes A 3/2 and A /2 remain comparable with each other, implying that hadronic helicity is not conserved at this range of Q 2 . The ratios E1+/M1+ obtained show, starting from a small and negative value at the real photon point, a clear tendency to cross zero, and to become positive with increasing Q 2 . This is a possible indication of a very slow approach toward the pQCD region. Furthermore, we find that the helicity amplitude A 1/2 and S 1/2 , but not A 3/2 , starts exhibiting the scaling behavior at about Q 2 ≥ 2.5(GeV/c) 2 .

We have analyzed the M (3/2) 1+ and E (3/2) 1+ multipole amplitudes of pion photoproduction in the framework of fixed-t dispersion relations. Applying the speed plot technique to our results for these multipoles, we have determined the position and the residues of the ∆ (1232) resonance pole. The pole is found at total c.m. energy W = (1211 − 50i) MeV on the second Riemann sheet, and the ratio of the electric and magnetic residues is R ∆ = −0.035 − 0.046i, resulting in an E2/M1 ratio for the "dressed" delta resonance of −3.5%.

A forward dispersion calculation is implemented for the spin polarizabilities γ 1 , · · · , γ 4 of the proton and the neutron. These polarizabilities are related to the spin structure of the nucleon at low energies and are structure-constants of the Compton scattering amplitude at O(ω 3 ). In the absence of a direct experimental measurement of these quantities, a dispersion calculation serves the purpose of constraining the model building, and of comparing with recent calculations in heavy baryon chiral perturbation theory.