Electromagnetic excitation of nucleon resonances

Recent progress on the extraction of electromagnetic properties of nucleon resonance excitation through pion photo- and electroproduction is reviewed. Cross section data measured at MAMI, ELSA, and CEBAF are analyzed and compared to the analysis of other groups. On this basis, we derive longitudinal and transverse transition form factors for most of the four-star nucleon resonances. Furthermore, we discuss how the transition form factors can be used to obtain empirical transverse charge densities. Contour plots of the thus derived densities are shown for the Delta, Roper, S ₁₁, and D ₁₃ nucleon resonances.     

Generalized polarizabilities and electroexcitation of the nucleon

Generalized nucleon polarizabilities for virtual photons can be defined in terms of electroproduction cross sections as function of the 4-momentum transfer Q². In particular, the sum of the generalized electric and magnetic polarizabilities Σ=α+β and the spin polarizability γ can be expressed by virtual photon absorption cross sections integrated over the excitation energy. These quantities have been calculated within the framework of the recently developed unitary isobar model for pion photo- and electroproduction on the proton, which describes the available experimental data up to an excitation energy of about 1 GeV. Our results have been compared to the predictions of chiral perturbation theory.     

Coherent pion electroproduction on the deuteron in the Δ(1232) resonance region

Coherent pion electroproduction on the deuteron is studied in the ((1232) resonance region in the impulse approximation, i.e., neglecting pion rescattering and two-body effects. The elementary reaction on the nucleon is described in the framework of an effective Lagrangian approach including the dominant P₃₃(1232) resonance and the usual background terms of the Born contributions for ?⁰ production. We have studied the influence of these different contributions on the various structure functions which determine the unpolarized exclusive differential cross section in a variety of kinematic regions.     

Parity violating pion electroproduction off the nucleon

Parity violating (PV) contributions due to interference betweenγ and Z⁰ exchange are calculated for pion electroproduction off the nucleon. A phenomenological model with effective Lagrangians is used to determine the resulting asymmetry for the energy region between threshold andΔ(1232) resonance. TheΔ resonance is treated as a Rarita-Schwinger field with phenomenological NΔ transition currents. The background contributions are given by the usual Born terms using the pseudovectorπN Lagrangian. Numerical results for the asymmetry are presented.     

Structure and Dynamical Evolution of Low Lying Nucleon Resonances

Within a multi-channels multi-resonances reaction model of pion nucleon reactions, we examine the properties of the nucleon resonances with masses less than 2?GeV. The Roper resonance and the second resonance in P ₁₁ are found to evolve dynamically from the same bare state. With the exception of the P ₁₃ and P ₃₁ resonances, our resonance pole positions agree well with the 3 and 4 star resonances listed by the Particle Data Group.     

Parity violation in pion electroproduction and photoproduction with a proton target

Parity violation in pion electroproduction and photoproduction on a proton target is investigated as a possible means of elucidating the structure of the electronic and non-leptonic neutral weak currents. We calculate both parity-violating effects caused directly by Z-boson exchange, which contributes only to electron scattering, and those due to parity-violating electromagnetic and nuclear interactions. The asymmetry in electroproduction is of order 20^?5, whereas that in photoproduction is ～10^?7. The sensitivity to the parameter sin²θ_w is investigated; it is a maximum at backward electron scattering angles. In addition to the Born terms, contributions from the Δ(1232) resonance and the light vector mesons [?(776) and ω(782)] are included in the model. Fits to the observed π⁰ and π⁺ electroproduction and photoproduction cross sections indicate that the model accounts for the production data in the medium energy region.     

Effective Lagrangian Approach to pion photoproduction from the nucleon

We present a pion photoproduction model on the free nucleon based on an Effective Lagrangian Approach (ELA) which includes the nucleon resonances (Δ(1232), N(1440), N(1520), N(1535), Δ(1620), N(1650), and Δ(1700)), in addition to Born and vector meson exchange terms. The model incorporates a new theoretical treatment of spin-3/2 resonances, first introduced by Pascalutsa, avoiding pathologies present in previous models. Other main features of the model are chiral symmetry, gauge invariance, and crossing symmetry. We use the model combined with modern optimization techniques to assess the parameters of the nucleon resonances on the basis of world data on electromagnetic multipoles. We present results for electromagnetic multipoles, differential cross-sections, asymmetries, and total cross-sections for all one pion photoproduction processes on free nucleons. We find overall agreement with data from threshold up to 1 GeV in laboratory frame.     

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 dominantS ₁₁(1535) resonance.This work has been supported by the Deutsche Forschungsgemeinschaft (SFB 201)     

The isobar model of the γN → ηN processes in the energy range from the threshold to 1200 MeV

The isobar model of the γN → γN processes is constructed on the basis of the precision measurements of the cross section for the γp → ηp process near the threshold in Mainz (Germany) and the sensational results of recent measurements of the Σ beam asymmetry and dσ/dΩ for this process in Grenoble (France). The model involves six nucleon resonances (MeV): S ₁₁(1535), S ₁₁(1650), P ₁₁(1440), P ₁₃(1720), D ₁₃(1520), and F ₁₅(1680). The properties of these resonances are discussed. The P ₁₃(1720) and F ₁₅(1680) resonances are responsible for large positive values of the Σ beam asymmetry for the γp → ηp reaction at small angles. The contribution of the S ₁₁(1650) resonance must be taken into account in addition to the contribution of the S ₁₁(1535) resonance in order to describe the experimental dependence of the total cross section on the photon energy. The values characterizing the γn → ηn reaction are calculated on the basis of the available data on the amplitudes of electromagnetic excitation of these resonances on protons and neutrons.     

Optimal bounds for the pion form factor from analyticity and experimental data

Optimal bounds for the pion electromagnetic form factor F(t) below threshold and on the pion mean-square charge radius 〈r_π²〉 = 6F'(0) are derived. Use is made of analyticity arguments and of experimental data on F(t) from e⁺e^? → π⁺π^? as well as e^?p → e^?nπ⁺. The method accounts in an approximate way for the statistical errors of the experimental information. Numerical results for F(t) are calculated for the CEA as well as the DESY electroproduction data.     

Study of nucleon spin-dependent properties in the resonance region

In this paper, the spin-dependent structure functions of nucleon g ₁, and photoabsorption cross sections σ_1/2, σ_3/2 and σ_T in the resonance region are estimated based on the constituent quark model and the properties of the five phenomenological Breit-Wigner resonances P ₃₃(1232), S ₁₁(1535), D ₁₃(1520), P ₁₁(1440), and F ₁₅(1680). Our results are compared to the recent E143 data of the polarized structure functions g ₁(W ², Q ²) at points Q ²=0.5 GeV² and Q ²=1.2 GeV² and the data of the total inclusive photoabsorption cross sections. Received: 7 October 1997     

Pion-nucleon vertex function with an off-shell nucleon

We present a model calculation for the π-N vertex function in the case in which there is a single off-mass-shell nucleon and a (nearly) on-mass-shell pion. We find very strong effects due to the P₁₁ resonance at 1470 MeV. We provide a simple parametrization of the vertex function in the case that at least one nucleon is on its mass shell.     

Analysis of pion electroproduction data in terms of a pion distribution function of the proton

Experimental data on the longitudinal π⁺ electroproduction on hydrogen have been analyzed in terms of a pion distribution function of the proton. This interpretation is based on the assumption that the pion can be considered as a parton in the nucleon for low momentum transfer Q². For the kinematical conditions photon mass Q² < 1 GeV² and electron energy loss ν > 2.2 GeV the pion electroproduction in the direction of the virtual photon can be viewed upon as quasielastic eπ⁺ → e′π⁺ scattering. Using the impulse approximation the pion distribution function of the proton can be deduced. According to the distribution function evaluated from pion electroproduction in the infinite momentum frame, the physical proton has a 3% admixture of the nπ⁺ state and the π⁺ in the nπ⁺ state carries 0.6% of the proton momentum.     

Implications of gauge invariance for pion electroproduction at threshold

We discuss the implications of gauge invariance in the problem of the on-shell extrapolation of the electroproduction low-energy theorems. We show that there is an invariant amplitude which can be evaluated at the Breit threshold either using gauge invariance and on-shell dispersion relations or following the Fubini and Furlan [5] extrapolation method starting from the current-algebra low-energy value of the amplitude. Comparing the two expressions, we find a relation between the electromagnetic pion form factor, F_π (k²), and the axial-vector nucleon form factors, g_A (k²) and h_A (k²).     

New possibilities for studying nucleon resonances in the production of π + π − pairs by polarized electrons on an unpolarized proton

The difference of the cross sections for double charged-pion production in the scattering of opposite-helicity electrons on an unpolarized proton is evaluated within the phenomenological model developed previously. The electromagnetic nucleon-resonance form factors and the parameters of nonresonance processes were taken from a fit to the latest data of the CLAS Collaboration on double charged-pion electroproduction. The effect of the longitudinal excitations of the P ₁₁(1440) and D ₁₃(1520) states on the difference of the helicity components of the cross section is studied. The sensitivity of this observable to the nucleon-resonance contribution opens the possibility of employing it both in extracting the Coulomb form factors and in seeking new baryon states. Signals from one of these states were possibly observed in the latest data of the CLAS Collaboration.     

Study of the baryon resonances structure via η photoproduction

Within a quark model the process γp → ηp, for E_γ^lab < 1.2 GeV, is investigated. We find that the recent data from GRAAL on the polarized beam asymmetry require significant contributions from the resonances D₁₃(1520), F₁₅(1680), and to a lesser extent from P₁₃(1720) in addition to those from the dominant S₁₁(1535) resonance, implied by the Mainz differential cross-section data. The contributions from the resonances S₁₁(1650), D₁₃(1700) and D₁₅(1675) are found consistently small but sensitive to the polarized target asymmetry measured recently at ELSA. These results are shown to be consistent with the quark model predictions.     

Pion electroproduction in the non-relativistic limit

Using a model based on the pseudovector Born terms, the Δ(1230) in the s- and u-channels, and the ω-meson, we have obtained pion electroproduction amplitudes from the nucleon in the non-relativistic limit. This model is an extension of the Blomqvist-Laget photopion production model and is in good agreement with experimental data for electron four-mornentum transfer squared up to approximately 0.3 GeV². The electropion production amplitudes we obtain may be used in the investigation of electropion production from nuclei.