Proton Form Factors Research Articles

Implications of the discrepancy between proton form factor measurements

Recent polarization transfer measurements of the proton electromagnetic form factors yield very different results from previous Rosenbluth extractions. This inconsistency implies uncertainties in our knowledge of the form factors and raises questions about how to best combine data from these two techniques. If the discrepancy is due to missing correction to the cross section data, as has been suggested, then different applications will require the use of different form factors. We present two extractions of the form factors: a global fit to the world's cross section data, and a combined extraction from polarization transfer and cross section data. The former provides a parametrization of the elastic electron-proton cross section, while the latter provides a consistent extraction of the underlying form factors, under the assumption that missing terms in the radiative correction explain the difference between the cross section and polarization transfer results.

Medium modification of the proton form factor

I argue that the double ratio of proton-recoil polarization-transfer coefficients, P'_x and P'_z, of the quasielastic 4He(e,e'p)3H reaction with respect to the elastic 1H(e,e'p) reaction is sensitive to possible medium modifications of the proton form factor in 4He. Recent measurements at both Mainz and Jefferson Lab of this double ratio at four-momentum transfers squared between between 0.4 GeV2 and 2.6 GeV2 are discussed. I show that the data challenge state-of-the-art conventional meson-nucleon calculations, as these are unable to describe the results. The data hint at the need to include medium modifications of the proton form factor, as predicted by a quark-meson-coupling model, in the calculations. A recently approved follow-up experiment at a Q2 of 0.8 GeV2 and 1.3 GeV2 with unprecedented precision will provide one of the most stringent tests of the applicability of various calculations.

The JLab polarization transfer measurements of proton elastic form factor

The ratio of the electric and magnetic proton form factors,GEpGMp, has been obtained in two Hall A experiments, from measurements of the longitudinal and transverse polarizations of the recoil proton,Pl andPt, in the elastic scattering of polarized electrons,\(\overrightarrow e p \to e\overrightarrow p \). Together these experiments cover theQ2 range of 0.5 to 5.6 GeV2. A new experiment is currently being prepared, to extend theQ2 range to 9 GeV2 in Hall C.

How to Reconcile the Rosenbluth and the Polarization Transfer Methods in the Measurement of the Proton Form Factors

The apparent discrepancy between the Rosenbluth and the polarization transfer methods for the ratio of the electric to magnetic proton form factors can be explained by a two-photon exchange correction which does not destroy the linearity of the Rosenbluth plot. Though intrinsically small, of the order of a few percent of the cross section, this correction is accidentally amplified in the case of the Rosenbluth method.

Constraints on medium modifications of nucleon form factors from quasielastic electron scattering

The quasielastic electron scattering contributions to the ${(e,e}^{\ensuremath{'}})$ and ${(e,e}^{\ensuremath{'}}p)$ reactions for medium and heavy nuclei depend on the nucleon electric and magnetic form factors in the nucleus. We investigate experimental data for the ${(e,e}^{\ensuremath{'}})$ reaction taken at SLAC on ${}^{12}\mathrm{C},$ ${}^{56}\mathrm{Fe},$ and ${}^{197}\mathrm{Au}$ at four-momentum transfers up to $0.28(\mathrm{GeV}{/c)}^{2}$ and for the ${(e,e}^{\ensuremath{'}}p)$ reaction at Jefferson Lab on ${}^{16}\mathrm{O}$ at four-momentum transfer of $0.8(\mathrm{GeV}{/c)}^{2}.$ Using a relativistic mean field ``single-particle'' theoretical model that successfully describes experimental data at lower energies and momentum transfers, we find no evidence for a modification of the nucleon form factors from their free space values for the inclusive ${(e,e}^{\ensuremath{'}})$ reactions and suggest that the exclusive reaction ${(e,e}^{\ensuremath{'}}p)$ with high precision data may provide an even tighter constraint on possible medium modifications of the proton form factors.

Polarization transfer in the 4He(e-->,e'p-->)3H reaction up to Q2=2.6 (GeV/c)2.

We have measured the proton recoil polarization in the 4He(e-->,e(')p-->)4H reaction at Q(2)=0.5, 1.0, 1.6, and 2.6 (GeV/c)(2). The measured ratio of polarization transfer coefficients differs from a fully relativistic calculation, favoring the inclusion of a medium modification of the proton form factors predicted by a quark-meson coupling model. In addition, the measured induced polarizations agree reasonably well with the fully relativistic calculation indicating that the treatment of final-state interactions is under control.

How well do we know the electromagnetic form factors of the proton?

Recent measurements of recoil polarization in elastic scattering have been used to extract the ratio of the electric to the magnetic proton form factors. These results disagree with Rosenbluth extractions from cross section measurements, indicating either an inconsistency between the two techniques, or a problem with either the polarization transfer or cross section measurements. To obtain precise knowledge of the proton form factors, we must first understand the source of this discrepancy.

Proton elastic form factor: The JLab data

The ratio of the electric and magnetic proton form factors, G Ep /G Mp , has been obtained in two Hall A experiments, from measurements of the longitudinal and transverse polarization of the recoil proton, PL and PT, respectively, in the elastic scattering of polarized electrons, $\vec{e}p\rightarrow e\vec{p}$ . Together these experiments cover the Q2 range 0.5 to 5.6 GeV2. A new experiment is currently being prepared, to extend the Q2 range to 9 GeV2 in Hall C.

Electromagnetic form factors of baryons and the Poincaré covariance

Preliminary results for the proton and neutron electromagnetic form factors, calculated within a front-form constituent quark model, are presented. A Poincaré covariant electromagnetic current operator for systems of interacting particles has been used and an effective quark mass at the photon-quark vertex has been introduced for a first insight of many body effects in the electromagnetic current.

Neutron densities from a global analysis of medium-energy proton-nucleus elastic scattering

A new method for extracting neutron densities from intermediate energy elastic proton-nucleus scattering observables uses a global Dirac phenomenological (DP) approach based on the Relativistic Impulse Approximation (RIA). Data sets for Ca40, Ca48 and Pb208 in the energy range from 500 MeV to 1040 MeV are considered. The global fits are successful in reproducing the data and in predicting data sets not included in the analysis. Using this global approach, energy independent neutron densities are obtained. The vector point proton density distribution is determined from the empirical charge density after unfolding the proton form factor. The other densities are parametrized. This work provides energy independent values for the RMS neutron radius, R_n and the neutron skin thickness, S_n, in contrast to the energy dependent values obtained by previous studies. In addition, the results presented in paper show that the expected rms neutron radius and skin thickness for Ca40 is accurately reproduced. The values of R_n and S_n obtained from the global fits that we consider to be the most reliable are given as follows: for Ca40 R_n is 3.314 > R_n > 3.310 fm and S_n is -0.063 > S_n > -0.067 fm; for Ca48 R_n is 3.459 > R_n > 3.413 fm and S_n is 0.102 > S_n > 0.056 fm; and for Pb208 R_n is 5.550 > R_n > 5.522 and S_n is 0.111 > S_n > 0.083 fm. These values are in reasonable agreement with nonrelativistic Skyrme Hartree-Fock models and with relativistic Hartree-Bogoliubov models with density-dependent meson-nucleon couplings. The results from the global fits for Ca48 and Pb208 are generally not in agreement with the usual relativistic mean-field models.

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 GE and GM. 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.

Instanton contribution to the proton and neutron electric form factors

We study the instanton contribution to the proton and neutron electric form factors. Using the single instanton approximation, we perform the calculations in a mixed time-momentum representation in order to obtain the form factors directly in momentum space. We find good agreement with the experimentally measured electric form factor of the proton. For the neutron, our result falls short of the experimental data. We argue that this discrepancy is due to the fact that we neglect the contribution of the sea quarks. We compare to lattice calculations and a relativistic version of the quark–diquark model.

Q2independence ofQF2/F1,Poincaré invariance, and the nonconservation of helicity

A relativistic constituent quark model is found to reproduce the recent data regarding the ratio of proton form factors, $F_2(Q^2)/F_1(Q^2)$. We show that imposing Poincare invariance leads to substantial violation of the helicity conservation rule, as well as an analytic result that the ratio $F_2(Q^2)/F_1(Q^2)\sim 1/Q$ for intermediate values of $Q^2$.

Covariant nucleon electromagnetic form factors from the Goldstone-boson-exchange quark model

We present a study of proton and neutron electromagnetic form factors for the recently proposed Goldstone-boson-exchange constituent quark model. Results for charge radii, magnetic moments, and electric as well as magnetic form factors are reported. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. All the predictions by the Goldstone-boson-exchange constituent quark model are found in remarkably good agreement with existing experimental data.

Polarization transfer in the 4He [formula omitted]H reaction

Polarization transfer in the 4He ( e → ,e′ p → ) 3 H reaction at a Q 2 of 0.4 (GeV/ c) 2 was measured at the Mainz Microtron MAMI. The ratio of the transverse to the longitudinal polarization components of the ejected protons was compared with the same ratio for elastic ep scattering. The results are consistent with a recent fully relativistic calculation which includes a predicted medium modification of the proton form factor based on a quark–meson coupling model.

Proton form factors in the hypercentral constituent quark model

We have calculated the ratio between the charge and magnetic form factors of the proton, making use of the hypercentral constituent quark model with relativistic corrections. The parameters of the model have been fixed in order to reproduce the baryon spectrum. The predicted values of this ratio are compared with the recent experimental results.

Current conservation in the covariant quark-diquark model of the nucleon

The description of baryons as fully relativistic bound states of quark and glue reduces to an effective Bethe-Salpeter equation with quark-exchange interaction when irreducible 3-quark interactions are neglected and separable 2-quark (diquark) correlations are assumed. This covariant quark-diquark model of baryons is studied with the inclusion of the quark substructure of the diquark correlations. In order to maintain electromagnetic current conservation it is then necessary to go beyond the impulse approximation. A conserved current is obtained by including the coupling of the photon to the exchanged quark and direct ``seagull'' couplings to the diquark structure. Adopting a simple dynamical model of constituent quarks and exploring various parametrisations of scalar diquark correlations, the nucleon Bethe-Salpeter equation is solved and the proton and neutron electromagnetic form factors are calculated numerically. The resulting magnetic moments are still about 50% too small, the improvements necessary to remedy this are discussed. The results obtained in this framework provide an excellent description of the electric form factors (and charge radii) of the proton, up to a photon momentum transfer of 3.5GeV^2, and the neutron.

Nucleon properties in the covariant quark-diquark model

In the covariant quark-diquark model the effective Bethe-Salpeter (BS) equations for the nucleon and the Δ are solved including scalar and axial vector diquark correlations. Their quark substructure is effectively taken into account in both, the interaction kernel of the BS equations and the currents employed to calculate nucleon observables. Electromagnetic current conservation is maintained. The electric form factors of proton and neutron match the data. Their magnetic moments improve considerably by including axial vector diquarks and photon induced scalar-axial vector transitions. The isoscalar magnetic moment can be reproduced, the isovector contribution is about 15% too small. The ratio µG E/G M and the axial and strong couplings g A, g πNN, provide an upper bound on the relative importance of axial vector diquarks confirming that scalar diquarks nevertheless describe the dominant 2-quark correlations inside nucleons.

FENICE results and a proposal for a new measurements of nucleon time-like form factors

The nucleon form factors have been extensively studied in the space-like region by several experiments. In the time-like region, only recently some precise measurements of the proton form factor became available and only one measurement of the neutron one has been performed by FENICE. In this paper, the main FENICE results are described, including the measurement of neutron and proton form factors and of the total e + e − → hadrons cross section close to the e +e − → N N threshold. The general behaviour of the neutron time-like form factors is rather unexpected. In the unphysical region, nucleon form factors have been studied by means of dispersion relations, using a model independent regularization method. No φ signal has been found, in contrast with some expectation about the strange quark content in the nucleon. However, large errors are present in these results, due to large errors in present data. In general, more data are demanded in order to have a complete knowledge of the time-like form factors of the neutron, experically close to the threshold, where there are some indications for a steep behaviour. A new experiment is proposed at SLAC in order to measure the nucleon form factors in the time-like region with the same accuracy than we have in the space-like one, disentangling the electric and magnetic contribution to the cross section.

The electromagnetic form factors of the free proton: Surprising new results from JLab

The ratio of the proton elastic electromagnetic form factors, G E G M , has been measured for Q 2 values from 0.5 to 3.5 (GeV/c) 2. The ratio was found to decrease with increasing Q 2, in contrast with an approximately constant value indicated by earlier experiments.