The role of the pion cloud in the interpretation of the valence light-cone wavefunction of the nucleon

The pion cloud renormalises the light-cone wavefunction of the nucleon which is measured in hard, exclusive photon-nucleon reactions. We discuss the leading twist contributions to high-energy exclusive reactions taking into account both the pion cloud and perturbative QCD physics. The nucleon’s electromagnetic form-factor at high Q² is proportional to the bare nucleon probability Z and the cross-sections for hard (real at large angle or deeply virtual) Compton scattering are proportional to Z². Our present knowledge of the pion-nucleon system is consistent with Z = 0.7 ± 0.2. If we apply just perturbative QCD to extract a light-cone wavefunction directly from these hard exclusive cross-sections, then the light-cone wavefunction that we extract measures the three valence quarks partially screened by the pion cloud of the nucleon. We discuss how this pion cloud renormalisation effect might be understood at the quark level in terms of the (in-)stability of the perturbative Dirac vacuum in low energy QCD.     

Form factors in lattice QCD

Lattice simulations of QCD have produced precise estimates for the masses of the lowest-lying hadrons which show excellent agreement with experiment. By contrast, lattice results for the vector and axial vector form factors of the nucleon show significant deviations from their experimental determination. We present results from our ongoing project to compute a variety of form factors with control over all systematic uncertainties. In the case of the pion electromagnetic form factor we employ partially twisted boundary conditions to extract the pion charge radius directly from the linear slope of the form factor near vanishing momentum transfer. In the nucleon sector we focus specifically on the possible contamination from contributions of higher excited states. We argue that summed correlation functions offer the possibility of eliminating this source of systematic error. As an illustration of the method we discuss our results for the axial charge, g _A , of the nucleon.     

Baryon structure from Lattice QCD

We present recent lattice results on the baryon spectrum, nucleon electromagnetic and axial form factors, nucleon to △ transition form factors as well as the △ electromagnetic form factors. The masses of the low lying baryons and the nucleon form factors are calculated using two degenerate flavors of twisted mass fermions down to pion mass of about 270 MeV. We compare to the results of other collaborations. The nucleon to △ transition and △ form factors are calculated in a hybrid scheme, which uses staggered sea quarks and domain wall valence quarks. The dominant magnetic dipole nucleon to △ transition form factor is also evaluated using dynamical domain wall fermions. The transverse density distributions of the △ in the infinite momentum frame are extracted using the form factors determined from lattice QCD.     

A Thomas-Fermi type picture and the electromagnetic structure of the nucleon

Using a Thomas-Fermi type picture of the nucleon as a dense system of quarks and antiquarks, we give a rationale for the ‘dipole’ nature, scaling and other characteristics of the nucleon electromagnetic form factors. Similar considerations are then given for the electromagnetic structure of the pion.     

Effects of bag surface motion with relativistic kinematics

Radial surface motion of the baryon bag is carried out in a model with relativistic kinematics, with confinement the result of volume energy and surface tension and the pion field coupled to the bag surface. We calculate radial wave functions for the nucleon, the Δ(1233) and the Roper resonance N^*(1450), which is identified as the first radial excitation of the nucleon.

Results are used to calculate form factors and pionic decay widths of the baryons examined. The approximations made in these calculations are discussed in extensio.     

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.     

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.     

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).     

The effective chiral Lagrangian from dimension-six parity and time-reversal violation

We classify the parity- and time-reversal-violating operators involving quark and gluon fields that have effective dimension six: the quark electric dipole moment, the quark and gluon chromo-electric dipole moments, and four four-quark operators. We construct the effective chiral Lagrangian with hadronic and electromagnetic interactions that originate from them, which serves as the basis for calculations of low-energy observables. The form of the effective interactions depends on the chiral properties of these operators. We develop a power-counting scheme and calculate within this scheme, as an example, the parity- and time-reversal-violating pion–nucleon form factor. We also discuss the electric dipole moments of the nucleon and light nuclei.     

Veneziano model for the ρ contribution to the nucleon form factors

The Igi-Veneziano model forπN scattering, combined with the experimental pion form factor is used to study theρ contribution to the isovector electromagnetic nucleon form factors.     

Elastic and inelastic form factors of baryons in a quark-potential-model

Starting from a Dirac equation with a scalar linear confinement potential for quarks we calculate the electromagnetic and weak form factors of the nucleon and the magnetic transition form factor of the Δ(1232). Taking the Lorentz transformation of the quark wave functions into account the results compare well with the experimental data.     

Electromagnetic form factors of the baryon octet in the perturbative chiral quark model

We apply the perturbative chiral quark model at one loop to analyze the electromagnetic form factors of the baryon octet. The analytic expressions for baryon form factors, which are given in terms of fundamental parameters of low-energy pion-nucleon physics (weak pion decay constant, axial nucleon coupling, strong pion-nucleon form factor), and the numerical results for baryon magnetic moments, charge and magnetic radii are presented. Our results are in good agreement with experimental data.Received: 7 January 2003, Revised: 4 November 2003, Published online: 15 April 2004PACS: 12.39.Ki Relativistic quark model - 13.40.Gp Electromagnetic form factors - 14.20.Dh Protons and neutrons - 14.20.Jn Hyperons     

Amplitude ambiguities in pion absorption on the diproton

A classification is given of, and intra-relationships are derived between amplitudes which yield identical spin-summed differential cross sections and vector polarizations for one of the nucleons emitted in pion absorption on the diproton. To accomplish this, a formal correspondence is established between the amplitude for pion absorption on the diproton and the amplitude for pion nucleon elastic scattering, and the well-known Minami ambiguity for the latter is generalized.Paper dedicated to the memory of Michael Moravcsik, whose untimely death terminated a very useful exchange of ideas onamplitude ambiguities, a subject on which he had been a leading authority. His remarks and observations provided me with a better, deeper insight into the topic of this paper     

NUCLEON PROPERTIES IN A QUARK BAG MODEL WITH WOODS-SAXON TYPE CONFINING POTENTIAL

A quark bag model with Woods-Saxon type confining potential is suggested. This model is used to examine three well-nown characteristic quantities of the nucleon and the proton electromagnetic form factors are evaluated by considering the quark core contributions. It is found that our model employing a confinement of W-S potential can improve the fit with the experimental values and can give good results for the form factors.     

Nucleon Form Factors and N-△ Transitions in a Hypercentral Constituent Quark Model with Meson Cloud

We study the nucleon form factors and the nucleon-△（1232） transitions in a framework of hypercentral constituent quark model. The pion meson cloud effect is taken into account explicitly. Our results show that the pion cloud contributes substantially to the nucleon form factors as well as to the helicity amplitudes of △（1232）, and it gives an improved agreement compared to the experimental.     

Properties of the nucleon in the nuclear medium within a chiral quark-meson theory

The modifications of the nucleon structure due to the presence of an external baryon medium are investigated in a chiral quark meson theory. To that end the Nambu-Jona-Lasinio (NJL) model is combined with the projected chiral soliton model. The medium effects are incorporated using the medium modified values of the pion decay constant and the pion and sigma masses at finite density. These values are evaluated within the NJL model. Using functional integral techniques the latter is solved in a quark continuum at finite density. The effective meson values serve to fix the parameters of the linear chiral sigma model which is solved in a variational projected mean field approach in order to obtain the nucleon properties. All nucleon properties show modifications in the medium except for the pion nucleon coupling constant. The proton radius shows an increase of 19% and the nucleon mass a decrease of 17% if the medium reaches nuclear matter density. The magnetic moments and axial vector coupling constant are less modified. All form factors show remarkable reduction at finite transfer momenta.     

A covariant view on the nucleons’ quark core

Established results for the quark propagator in Landau gauge QCD, together with a detailed comparison to lattice data, are used to formulate a Poincaré-covariant Faddeev approach to the nucleon. The resultant three-quark amplitudes describe the quark core of the nucleon. The nucleon’s mass and its electromagnetic form factors are calculated as functions of the current quark mass. The corresponding results together with charge radii and magnetic moments are discussed in connection with the contributions from various ingredients in a consistent calculation of nucleon properties, as well as the role of the pion cloud in such an approach.