Electroexcitation of nucleon resonances

In these lectures the status of electromagnetic excitation of nucleon resonances is reviewed and some of the open problems of the structure and spectroscopy of light-quark baryons are discussed. The basic formalism for describing electromagnetic processes is introduced but not derived.Lecture given at the 8th Summer School on Intermediate-Energy Physics: Hadron Dynamics at Low and Intermediate Energies, Prague, July 10–14, 1995.     

Baryon resonance analysis from MAID

The unitary isobar model MAID2007 has been used to analyze the recent data of pion electroproduction. The model contains all four-star resonances in the region below W = 2 GeV and both single-Q~2 and Q~2 dependent transition form factors could be obtained for the Delta, Roper, D_(13)(1520), S_(11) (1535), S_(31) (1620), S_(11)(1650), D_(15)(1675), F_(15)(1680) and P_(13)(1720). From the complete world data base, including also π~- data on the neutron, also Q~2 dependent neutron form factors are obtained. For all transition form factors we also give convenient numerical parameterizations that can be used in other reactions. Furthermore, we show how the transition form factors can be used to obtain empirical transverse charge densities and our first results are given for the Roper, the S_(11) and D_(13) resonances.     

Baryon resonance analysis from MAID

The unitary isobar model MAID2007 has been used to analyze the recent data of pion electroproduction. The model contains all four-star resonances in the region below W = 2 GeV and both single-Q2 and Q2 dependent transition form factors could be obtained for the Delta, Roper, D13（1520）, S11 （1535）, S31 （1620）, $11（1650）, D15（1675）, F15（1680） and P13（1720）. From the complete world data base, including also π data on the neutron, also Q2 dependent neutron form factors are obtained. For all transition form factors we also give convenient numerical parameterizations that can be used in other reactions. Furthermore, we show how the transition form factors can be used to obtain empirical transverse charge densities and our first results are given for the Roper, the S11 and D13 resonances.     

The nucleon as a QCD bound state in a Faddeev approach

Established results for the quark propagator of Landau gauge QCD, together with a detailed comparison to lattice data, are implemented in a Poincaré-covariant Faddeev approach to the nucleon. The nucleon mass and its electromagnetic form factors, together with charge radii and magnetic moments, are calculated as a function of the current-quark mass. The role of the pion cloud is discussed.     

Strange quarks in the nucleon sea

The HAPPEX Collaboration measured parity-violating electron scattering from ⁴He$(e, e)$and H(e, e) in 2004 and 2005 for Q ²≤0.11GeV^2. Results for the strange-quark contributions to the electromagnetic form factors of the nucleon from the 2004 data will be reviewed. Preliminary results from the 2005 data, which have significantly greater statistical precision, are G _E ^s = 0.004±0.014_stat±0.013_syst for Q ² = 0.0772GeV^2 from the helium data and G _E ^s +0.088G _M ^s = 0.004±0.011_stat±0.005_syst±0.004_FF for Q ² = 0.1089GeV^2 from the hydrogen data.     

Probing nucleon structure on the lattice

The QCDSF/UKQCD Collaboration has an ongoing program to calculate nucleon matrix elements with two flavours of dynamical O(a) improved Wilson fermions. Here we present recent results on the electromagnetic form factors, the quark momentum fraction 〈x〉 and the first three moments of the nucleon's spin-averaged and spin-dependent generalised parton distributions, including preliminary results with pion masses as low as 320MeV.     

Dependence of electromagnetic form factors of hadrons on light-cone frames

A constituent quark model is developed for an arbitrary light-cone direction so that the light-front time is x_LF⁺ = ω · x with a constant lightlike four-vector ω. Form factors are obtained from free one-body electromagnetic current matrix elements. They are found to be ω-independent for spin-0 mesons, nucleons and the Λ-hyperon, while there is an ω-dependence for spin-1 systems like the deuteron.     

Sensitivity of the pQCD deuteron structure to the nucleon form factors

We discuss the applicability of pQCD to the elastic scattering of electrons on protons and deuterons. We analyze the Q²-dependence of the reduced deuteron form factor, taking into account the recent data on the electric proton form factor and we find that the value of the QCD-scale parameter Λ differs essentially from the value Λ = 0.1 GeV, previously found using the dipole parametrization of the electromagnetic nucleon form factors G_E and G_M. Moreover, the predicted scaling behavior of the reduced deuteron form factor cannot be recovered in the Dirac and Pauli representations for the nucleon electromagnetic form factors. Received: 14 October 2002 / Accepted: 12 November 2002 / Published online: 11 March 2003 RID="a" ID="a"Permanent address: National Science Center KFTI, 310108 Kharkov, Ukraine. RID="b" ID="b"e-mail: etomasi@cea.fr Communicated by V.V. Anisovich     

Asymptotic behavior of nucleon electromagnetic form factors in time-like region

We study the asymptotic behavior of the ratio of Pauli and Dirac electromagnetic nucleon form factors, F₂/F₁, in time-like region, for different parametrizations built for the space-like region. We investigate how fast the ratio F₂/F₁ approaches the asymptotic limits according to the Phragmèn-Lindel?f theorem. We show that the QCD-inspired logarithmic behavior of this ratio results in very far asymptotics, experimentally unachievable. This is also confirmed by the normal component of the nucleon polarization, P_y, in e⁺ + e^-↦N + ˉ (in collisions of unpolarized leptons), which is a very interesting observable, with respect to this theorem. Finally we observe that the 1/Q parametrization of F₂/F₁ contradicts this theorem.     

Logarithmic corrections and soft photon phenomenology in the multipole model of the nucleon form factors

We analyzed the presently available experimental data on nucleon electromagnetic form factors within a multipole model based on dispersion relations. A good fit of the data is achieved by considering the coefficients of the multipole expansions as logarithmic functions of the momentum transfer squared. The superconvergence relations, applied to this coefficients, makes the model agree with unitary constraints and pQCD asymptotics for the Dirac and Pauli form factors. The soft photon emission is proposed as a mechanism responsible for the difference between the Rosenbluth, polarization and beam-target asymmetry data. It is shown that the experimentally measured cross-sections depend not only on the Dirac and Pauli form factors, but also on the average number of the photons emitted. For the proton this number is shown to be different for different types of experimental measurements and then estimated phenomenologically. For the neutron the same mechanism predicts that the data form different types of experiments must coincide with high accuracy. A joint fit of all the experimental data reproduce the Q²-dependence with the accuracy χ²/dof = 0.86 . Predictions of the model, that 1) the ratios of the proton form factors G _E/G _M are different for Rosenbluth, polarization and beam-target asymmetry experiments and 2) similar ratios are nearly the same for neutron, can be used for experimental verification of the model.     

Electromagnetic transitions of low-lying nucleon resonances in point form relativistic quantum mechanics

Point form relativistic quantum mechanics is employed to calculate the electromagnetic transition amplitudes of low-lying nucleon resonances. The results obtained are compared with the non-relativistic approach and other model calculations. Differences among them are discussed.     

Electroexcitation of Low-Lying Particle-Hole RPA States of 16O with WBP Interaction

The nuclear structure of ¹⁶O is studied in the framework of the particle-hole random phase approximation (ph RPA). The Hamiltonian is diagonalized within a model space with particle orbits {1d_5/2,1d_3/2 , and 2s_1/2} and the hole orbits {1p_3/2 and 1p_1/2} using Warburton and Brown interaction WBP. The ph RPA calculations are tested, by comparing the electron scattering form factors with the available experimental data. The results of electron scattering form factors and reduced transition strength for the states: 1^-, T=0 (7.116 MeV); 2^-, T=1 (12.968 MeV); 2^-, T=1 (20.412 MeV); and 3^-, T=0 (6.129 MeV) are interpreted in terms of the harmonic-oscillator (HO) wave functions of size parameter b. The occupation probabilities of the single particle and hole orbits are calculated. The spurious states are removed by adding the center of mass (CM) correction to the nuclear Hamiltonian. A comparison with the available experiments data is presented.     

Phase motion of baryon resonances

A novel technique to probe the resonant structure of a partial-wave amplitude is proposed and applied to data on photoproduction of baryon resonances.     

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.     

In-medium properties of nucleon resonances

Recent experimental results for the in-medium properties of nucleon resonances are discussed. The experiments were done with the TAPS detector at the tagged photon beam of the MAMI accelerator in Mainz. Measured was the photoproduction of mesons (final states π⁰X, ηX, 2π⁰X and π⁰π^±X) from the nuclei ¹²C, ⁴⁰Ca, ⁹³Nb and ²⁰⁸Pb up to the second resonance region. The results were analyzed in view of the in-medium properties of the P₃₃(1232), the D₁₃(1520), and the S₁₁(1535) resonances.