D. Drechsel

A unitary isobar model for pion photo- and electroproduction on the proton up to 1 GeV☆

Abstract 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 Q2 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.

Unitary Isobar Model - MAID2007

Abstract.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 2GeV 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 2GeV. Because of its inherent simplicity, MAID2007 is well adopted for predictions and analysis of the observables in pion photo- and electroproduction.

Dispersion relations in real and virtual Compton scattering

Abstract 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.

An isobar model for η photo- and electroproduction on the nucleon

An isobar model containing Born terms, vector meson exchange and nucleon resonances is used to analyze recent eta photoproduction data for cross section and beam asymmetry, as well as JLab electroproduction data. Good overall description is achieved up to Q^2 = 4.0 (GeV/c)^2. Besides the dominant S11(1535) resonance, we show that the second S11 resonance, S11(1650), is also necessary to be included in order to extract S11(1535) resonance parameters properly. In addition, the beam asymmetry data allow us to extract very small ( eta N decay branching ratios of D13(1520) and F15(1680) resonances because of the overwhelming s-wave dominance. The model is implemented as a part of the MAID program.

MULTIPOLE ANALYSIS OF PION PHOTOPRODUCTION BASED ON FIXED T DISPERSION RELATIONS AND UNITARITY

Abstract 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 Omnes and Muskhelishvili. The free parameters were determined by a fit to the most recent data for π + and π 0 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 M 1− connected with the Roper resonance P 11 (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.

Photo- and electroproduction of eta mesons

Eta photo- and electroproduction off the nucleon is investigated in an effective lagrangian approach that contains Born terms and both vector meson and nucleon resonance contributions. In particular, we review and develop the formalism for coincidence experiments with polarization degrees of freedom. The different response functions appearing in single and double polarization experiments have been studied. We will present calculations for structure functions and kinematical conditions that are most sensitive to details of the lagrangian, in particular with regard to contributions of nucleon resonances beyond the dominantS11(1535) resonance.

Measurement of the πmeson polarizabilities via the γp → γπ + n reaction

Abstract.An experiment on the radiative π{+}-meson photoproduction from the proton ( γp → γπ{+}n) was carried out at the Mainz Microtron MAMI in the kinematic region 537MeV < Eγ < 817MeV, 140°≤

Gerasimov-Drell-Hearn sum rule and related integrals

\theta_{{\gamma \gamma ^{\prime }}}^{{{{\rm cm}}}}

Dispersion-theoretical analysis of the nucleon electromagnetic form factors: Inclusion of time-like data

≤180°. The π{+}-meson polarizabilities have been determined from a comparison of the data with the predictions of two different theoretical models, the first one being based on an effective pole model with pseudoscalar coupling while the second one is based on diagrams describing both resonant and nonresonant contributions. The validity of the models has been verified by comparing the predictions with the present experimental data in the kinematic region where the pion polarizability contribution is negligible ( s1 < 5mπ2) and where the difference between the predictions of the two models does not exceed 3%. In the region, where the pion polarizability contribution is substantial ( 5 < s1/mπ2 < 15, -12 < t/mπ2 < - 2), the difference

Electromagnetic excitation of nucleon resonances

\ensuremath{(\alpha -\beta )_{\pi^{+}}}