Electromagnetic nucleon form factors in the spacelike region

Use of the double-polarization technique to obtain the elastic nucleon form factors has resulted in a dramatic improvement of the quality of two of the four nucleon electromagnetic form factors, GEp and GEn. It has also changed our understanding of the proton structure, having resulted in a distinctly different Q2-dependence for both GEp and GMp, contradicting the prevailing wisdom of the 1990’s based on cross section measurements, namely that GEp and GMp obey a “scaling” relation μGEp ∼ GMp. A related consequence of the faster decrease of GEp revealed by the Jefferson Lab (JLab) polarization results was the disappearance of the early scaling F2/F1 ∼ 1/Q2 predicted by perturbative QCD. In three experiments, GEp(1), GEp(2) and GEp(3), in Halls A and C at JLab, the ratio of the proton’s electromagnetic elastic form factors, GEp/GMp, was measured up to four momentum transfer Q2 of 8.5 GeV2 with high precision, using the recoil polarization technique. The initial discovery that the proton form factor ratio measured in these three experiments decreases approximately linearly with four-momentum transfer, Q2, for values above ∼ 1 GeV2, was modified by the GEp(3) results, which suggests a slowing down of this decrease. There is an approved experiment, GEp(5), to continue these measurements to 15 GeV2. A dedicated experimental setup, the super bigbite spectrometer (SBS), will be built for this purpose. It will be equipped with a new focal plane polarimeter to measure the polarization of the recoil protons. In this presentation, I will review the status of the proton elastic electromagnetic form factors, mention succinctly a number of theoretical approaches to describe results and show some features required for the future GEp(5) experiment.

Effects of neutrino magnetic moment and charge radius constraints and medium modifications of the nucleon form factors on the neutrino mean free path in dense matter

We present recent lattice results on the baryon spectrum, nucleon electromagnetic and axial form factors, nucleon to Δ transition form factors as well as the Δ 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 Δ transition and Δ form factors are calculated in a hybrid scheme, which uses staggered sea quarks and domain wall valence quarks. The dominant magnetic dipole nucleon to Δ transition form factor is also evaluated using dynamical domain wall fermions. The transverse density distributions of the Δ in the infinite momentum frame are extracted using the form factors determined from lattice QCD.

Nucleon and pion electromagnetic form factors in a light-front constituent quark model

In a recent letter we suggested that the momentum dependence of the exact meson propagator may be responsible for the dipole-like behavior of the nucleon electromagnetic form factors over the limited range of data available. In this paper we extend the analysis to include more than one vector-meson propagator, and, by assuming a simplified form for the imaginary part of the level shift, we calculate the form factors explicitly. The nucleon electromagnetic form-factor data are fitted for momentum transfer to $2\frac{\mathrm{GeV}}{c}$ assuming just one isovector-vector meson and two isoscalar-vector mesons. The resulting fit is much better than that obtained using the dipole formula, and min ${\ensuremath{\chi}}^{2}$ occurs for values of the masses and widths of the vector mesons close to the experimental values of the $\ensuremath{\rho}$, $\ensuremath{\omega}$, and $\ensuremath{\phi}$ resonances. The six independent meson-nucleon coupling constants are determined. Their values are consistent with the assumption that the nucleon charge and the magnetic moment distributions are extended, that is, that there are no hard-core contributions to the form factors. This assumption completely determines the isovector coupling constants and reduces the number of independent coupling constants to two. The pion and kaon charge form factors, as deduced from the nucleon charge form factors assuming universality, are compared with the available data. The pion form factors fit the data in both the spacelike and the timelike regions, including the resonance shape for the $\ensuremath{\rho}$ contribution to the pion form factor. The kaon form-factor data disagree with the assumption of universality in both the spacelike and timelike regions.

The spectroscopy of light and strange baryons and elastic electromagnetic form factors of nucleon have been studied through a simple semi-relativistic quark model. For SU(6)-invariant part of spectrum, we treated the baryons as a spin-independent three-body bound system and presented the exact analytical solution of three-body Klein–Gordon equation. Considering the SU(6)-invariant interaction as a combination of scalar linear and vector Coulombic-like potentials, we obtained analytical formulas for energy levels and the hyperradial wave functions which have been employed in the calculations of the mass spectrum of baryons, electromagnetic elastic form factors, and charge radii of nucleon. The evaluated observables have been compared with experimental data, and it has been shown that the present model leads to a fairly good description of the observed resonances.

Evaluation of fermion loops applied to the calculation of the [formula omitted] mass and the nucleon scalar and electromagnetic form factors

Electromagnetic form factors of the nucleon

Pole dominance and a Veneziano model for the scattering amplitudes πN→πN, πN→NA1 and πN→Nρ are used to derive the electromagnetic nucleon form factors. The technique is based on a method proposed by Rosner and Suura. Correction terms to the pole-dominance assumption are necessary and therefore included. Their specific form strongly influences the final result. With the simplest assumptions for them the electric form factor contains a dipole term instead of an infinite sequence of poles as encountered in the meson case, and drops off at infinity liket−1. However to get a reasonable magnetic form factor some correction terms have to be modified. As a by-product an expression for the axial form factor is obtained.

We investigate the procedure which one uses to calculate the nucleon form factors, for both the electromagnetic and axial-vector currents, from bag models. We first point out that these form factors, as functions of ${q}^{2}$ alone, can in general be expressed in terms of several matrix elements, all of which are defined in the Breit frame. We then evaluate these Breit-frame matrix elements by assuming both (1) that the current operators can be approximated by the one-body quark contribution, and (2) that the nucleon wave functions at rest can be approximated by those given in the MIT bag model. Typical numerical results, as augmented by pionic corrections, provide a reasonable description of the experimental data.

Theoretical implications of the suggestion that the observed nucleon electromagnetic form factors indicate the existence of a nucleon "core" are discussed. On the basis of physical arguments concerning the nature of such a core, it is shown that, for the neutron, both the charge form factor, ${{F}_{\mathrm{ch}}}^{n}({q}^{2})$, and the magnetic form factor, ${{F}_{\mathrm{mag}}}^{n}({q}^{2})$, must vanish as ${q}^{2}$, the invariant momentum transfer, increases without limit. On the other hand, for the proton ${{F}_{\mathrm{ch}}}^{p}({q}^{2})\ensuremath{\rightarrow}{{Z}_{2}}^{(s)}$ and ${{F}_{\mathrm{mag}}}^{p}({q}^{2})\ensuremath{\rightarrow}\frac{{{Z}_{2}}^{(s)}}{2M}$, where ${{Z}_{2}}^{(s)}$ is the wave function renormalization constant for strong interactions, which is a measure of the probability of the "core state." In terms of the Dirac form factor, ${F}_{1}({q}^{2})$, and the Pauli form factor, ${F}_{2}({q}^{2})$, these results read ${{F}_{1}}^{n}({q}^{2})\ensuremath{\rightarrow}0$, ${{F}_{1}}^{p}({q}^{2})\ensuremath{\rightarrow}{{Z}_{2}}^{(s)}$, and ${q}^{2}{F}_{2}({q}^{2})\ensuremath{\rightarrow}0$ for both neutron and proton. The results for ${F}_{1}({q}^{2})$ are the same as those obtained by Hiida, Nakanishi, Nogami, and Uehara. The other result implies the existence of a relationship which may be used to eliminate one parameter in the analysis of ${F}_{2}$. The generality of the interpretation of ${F}_{\mathrm{ch}}$ and ${F}_{\mathrm{mag}}$ as Fourier transforms of distributions of charge and magnetization, respectively, is demonstrated in the Appendix.

Four-fermion operators have been utilized in the past to link the quark-exchange processes in the interaction of hadrons with the effective meson-exchange amplitudes. In this presentation, we apply the similar idea of Fierz rearrangement to the electromagnetic processes and focus on the electromagnetic form factors of nucleon and electron. We explain the motivation of using four-fermion operators and discuss the advantage of this method in computing electromagnetic processes.

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 proton this number is shown to be different for different types of experimental measurements and then estimated phenomenologically. For 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 $Q^2-$dependence with the accuracy $\chi^2/dof=0.86$. 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.

We investigate a new method of extracting nucleon form factors by using measured asymmetries of polarized leptons scattered off polarized targets. Systematic errors can be eliminated that way, unlike the conventional analysis via Rosenbluth plots. The kinematics can be chosen such that the asymmetry receives contributions selectively from either ${G}_{M}^{2}$(${q}^{2}$) or ${G}_{E}$(${q}^{2}$)${G}_{M}$(${q}^{2}$). The latter combination allows a better determination of ${G}_{M}$(${q}^{2}$) for small ${q}^{2}$. We also discuss lepton mass effects in d\ensuremath{\sigma}/d\ensuremath{\Omega}. While such mass effects reduce the suppression of magnetic contributions to d\ensuremath{\sigma}/d\ensuremath{\Omega} for small ${q}^{2}$, they do not in general result in a greater sensitivity of d\ensuremath{\sigma}/d\ensuremath{\Omega} or of the longitudinal asymmetries to a variation of the magnetic form factor, unless one chooses specific kinematics, as is demonstrated here. The transverse asymmetry, however, displays naturally a greater sensitivity to ${G}_{M}$(${q}^{2}$) for the muon as compared to the electron. Such experiments are feasible at both the electron facilities (Bates, CEBAF, MAMI, and ELSA) and the muon facilities (SIN, TRIUMF, and LAMPF). Constituent models of the nucleon (quark confinement models) emphasize the low -${q}^{2}$ region of the form factors, where data presently are still incomplete. This has implications for the study of the nuclear response function in quasifree scattering (\ensuremath{\mu},\ensuremath{\mu}'p) from nuclei using polarized muons.

The BESIII experiment, operated at the BEPCII e+e- collider in Beijing, has acquired large data sets at center-of-mass energies between 2.0 GeV and 4.6 GeV. One of the key aspects of the physics program of the BESIII collaboration is to test the understanding of QCD at intermediate energies. Applying different experimental techniques, form factors of hadrons are measured. Among these are the pion form factor, as an important input to the (g - 2)μ puzzle, and the electro-magnetic form factors of nucleons and hyperons in the time-like regime. An overview of the recent results and some ongoing studies at BESIII is provided.