The unitary isobar model MAID2007 has been developed to analyze the world data of pion photo-and electroproduction. The model contains both a common background and several resonance terms. The background is unitarized according to the K-matrix prescription, and the 13 four-star resonances with masses below 2 GeV are described by appropriately unitarized Breit-Wigner forms. The data have been analyzed by both single-energy and global fits, and the transverse and longitudinal helicity amplitudes have been extracted for the four-star resonances below 2 GeV. Because of its inherent simplicity, MAID2007 is well adopted for predictions and analysis of the observables in pion photo-and electroproduction.

Dispersion relations allow for a coherent description of the nucleon electromagnetic form factors measured over a large range of momentum transfer, Q 2 ≃ 0 . . . 35 GeV 2 . Including constraints from unitarity and perturbative QCD, we present a novel parametrisation of the absorptive parts of the various isoscalar and isovector nucleon form factors. Using the current world data, we obtain results for the electromagnetic form factors, nucleon radii and meson couplings. We stress the importance of measurements at large momentum transfer to test the predictions of perturbative QCD.#1 Work supported in part by the Deutsche Forschungsgemeinschaft (SFB 201).

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.

A unified presentation is given on the use of dispersion relations in the real and virtual Compton scattering processes off the nucleon. The way in which dispersion relations for Compton scattering amplitudes establish connections between low energy nucleon structure quantities, such as polarizabilities or anomalous magnetic moments, and the nucleon excitation spectrum is reviewed. We discuss various sum rules for forward real and virtual Compton scattering, such as the Gerasimov-Drell-Hearn sum rule and its generalizations, the Burkhardt-Cottingham sum rule, as well as sum rules for forward nucleon polarizabilities, and review their experimental status. Subsequently, we address the general case of real Compton scattering (RCS). Various types of dispersion relations for RCS are presented as tools for extracting nucleon polarizabilities from the RCS data. The information on nucleon polarizabilities gained in this way is reviewed and the nucleon structure information encoded in these quantities is discussed. The dispersion relation formalism is then extended to virtual Compton scattering (VCS). The information on generalized nucleon polarizabilities extracted from recent VCS experiments is described, along with its interpretation in nucleon structure models. As a summary, the physics content of the existing data is discussed and some perspectives for future theoretical and experimental activities in this field are presented.

Eta photo-and electroproduction on the nucleon is studied using an isobar model. The model contains Born terms, and contributions from vector meson exchanges and nucleon resonances. Our results are compared with recent eta photoproduction data for differential and total cross sections, beam asymmetry, and target asymmetry, as well as electroproduction data. Besides the dominant S 11 (1535) resonance, we show that the second S 11 resonance, S 11 (1650), is also necessary to be included in order to extract S 11 (1535) resonance parameters properly. In addition, the beam asymmetry data allow us to extract very small (< 0.1%) N * → ηN decay branching ratios of the D 13 (1520) and F 15 (1680) resonances because of the overwhelming swave dominance. This model (ETA-MAID) is implemented as a part of the MAID program 1 .

The spin structure of the nucleon resonance region is analyzed on the basis of our phenomenological model MAID. Predictions are given for the Gerasimov-Drell-Hearn sum rule as well as generalized integrals over spin structure functions. The dependence of these integrals on momentum transfer is studied and rigorous relationships between various definitions of generalized Gerasimov-Drell-Hearn integrals and spin polarizabilities are derived. These results are compared to the predictions of chiral perturbation theory and phenomenological models.

We analyze virtual Compton scattering off the nucleon at low energies in a covariant, model-independent formalism. We define a set of invariant functions which, once the irregular nucleon pole terms have been subtracted in a gauge-invariant fashion, is free of poles and kinematical zeros. The covariant treatment naturally allows one to implement the constraints due to Lorentz and gauge invariance, crossing symmetry, and the discrete symmetries. In particular, when applied to the ep → e ′ p ′ γ reaction, charge-conjugation symmetry in combination with nucleon crossing generates four relations among the ten originally proposed generalized polarizabilities of the nucleon. 13.60.Fz,14.20.Dh Typeset using REVT E X * This work was supported by the Deutsche Forschungsgemeinschaft (SFB 201)

A reggeized model for η and η ′ photoproduction on the nucleon is presented. In this model, t-channel vector meson exchanges are described in terms of Regge trajectories to comply with the correct high energy behavior. We compare this reggeized model with an isobar model (η-MAID), where the t-channel exchanges are described by ρ and ω poles. Both models contain the same resonance contributions, and describe current γp → ηp data up to E lab γ = 2 GeV quite well, but only the reggeized model can be successfully extended to higher energies. For the γp → η ′ p reaction, the reggeized model is found to be able to give a satisfactory description. For the differential cross section data from SAPHIR, we find that the observed linear forward rise in cos θ near E lab γ = 1.6 GeV can be well described by the interference of an S 11 resonance and the Regge trajectory exchanges without any need for an additional P -wave resonance.