Electron-proton Elastic Scattering Cross Sections Research Articles

New extraction of the Re+e− elastic scattering cross-section ratio based on a simplified phenomenological hard two-photon-exchange correction approach

In this work, we present a prediction of the positron-proton and electron-proton elastic scattering cross-section ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ based on a new phenomenological parametrization of the hard two-photon-exchange (TPE) corrections to electron-proton elastic scattering cross section ${\ensuremath{\sigma}}_{R}$. The TPE parametrization proposed in this work is rather simple, as it only requires the use of suitable global fits of both the Rosenbluth magnetic ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}_{M}$, and the true magnetic ${G}_{M}$ form factors, or alternatively, the electric form factors ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}_{E}$ and ${G}_{E}$. We compare our results to recent extractions, and world's data on ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ with emphasis mainly on the kinematics range of the recent direct measurements from the CLAS, VEPP-3, and OLYMPUS experiments. With the proper choice of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}_{M}$ and ${G}_{M}$ parametrizations, and while our results are in generally good agreement with ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ measurements taken at high $\ensuremath{\varepsilon}$ points and for all ${Q}^{2}$ range, they agree remarkably well, within the error bands of the predictions, with ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ measurements taken at low-$\ensuremath{\varepsilon}$ points for ${Q}^{2}=1.0$ and $1.5\phantom{\rule{0.16em}{0ex}}{(\mathrm{GeV}/\mathrm{c})}^{2}$, where emphasis should be placed for evidence of hard TPE correction. Finally, we believe that the assumption that hard TPE corrections could account for the discrepancy on the proton's form factors ratio ${\ensuremath{\mu}}_{p}{G}_{E}/{G}_{M}$ is still an open question as more measurements of ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ are clearly needed for ${Q}^{2}>\phantom{\rule{4pt}{0ex}}2.1\phantom{\rule{0.16em}{0ex}}{(\mathrm{GeV}/\mathrm{c})}^{2}$, in the region where the discrepancy is significant.

Extraction of elastic scattering cross-section ratio Re+e− from ep elastic scattering experimental data

In this work, we present a new prediction of the positron-proton to electron-proton elastic scattering cross sections ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$. While many phenomenological studies extracted the ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ using proposed, model-independent parametrizations of the hard two-photon exchange (TPE) corrections to electron-proton ($\text{ep}$) elastic scattering cross section ${\ensuremath{\sigma}}_{R}$, we do not assume prior knowledge of the functional form of the hard TPE corrections to ${\ensuremath{\sigma}}_{R}$, and use combined unpolarized, and polarized $\text{ep}$ elastic scattering experimental data to extract the TPE contributions. We provide a simple parametrization of the TPE corrections to ${\ensuremath{\sigma}}_{R}$, along with the uncertainties associated with the model dependence of the extractions, and use our TPE parametrization to predict the ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$. We compare our prediction of ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ to several previous phenomenological extractions, TPE-hadronic calculations, and world's data with emphasis mainly on the kinematics range of the recent precise direct measurements from the CLAS, VEPP-3, and OLYMPUS experiments.

New prediction of elastic scattering cross sections ratio Re+ e− based on phenomenological two-photon exchange corrections

The proton’s electric and magnetic form factors (FFs) and their ratio Rp = are fundamental and essential ingredients needed to parametrize the internal structure of the proton as well as many composite particles. However, the inconsistency in the results reported on these FFs and their ratio as measured by the Rosenbluth method and the polarization transfer method has led the community to believe that such a discrepancy is due to a systematic difference between the two methods. It was proposed that missing higher order radiative correction to the electron-proton elastic scattering cross section σR (ϵ, Q 2) and in particular two-photon exchange correction (TPE) should be applied in order to reconcile these measurements. The effect of TPE on electron-proton scattering observables was studied extensively in the last few years. However, the most direct method for measuring TPE contributions is the comparison of positron-proton and electron-proton elastic scattering cross sections ratio Re+ e− (ϵ, Q 2). In this proceedings, I present a new prediction of the ratio Re+ e− as determined using a new parametrization of TPE corrections to σR . I then compare my results to several previous phenomenological extractions, TPE hadronic calculations, and previous and recent direct measurements of Re+ e− .

Precise determination of the proton magnetic radius from electron scattering data

We extract the proton magnetic radius from the high-precision electron-proton elastic scattering cross section data. Our theoretical framework combines dispersion analysis and chiral effective field theory and implements the dynamics governing the shape of the low-$Q^2$ form factors. It allows us to use data up to $Q^2\sim$ 0.5 GeV$^2$ for constraining the radii and overcomes the difficulties of empirical fits and $Q^2 \rightarrow 0$ extrapolation. We obtain a magnetic radius $r_M^p$ = 0.850 $\pm$0.001 (fit 68%) $\pm$0.010 (theory full range) fm, significantly different from earlier results obtained from the same data, and close to the extracted electric radius $r_E^p$ = 0.842 $\pm$0.002 (fit) $\pm$0.010 (theory) fm.

Hard two-photon contribution to elastic lepton-proton scattering determined by the OLYMPUS experiment

The OLYMPUS collaboration has recently made a precise measurement of the positron-proton to electron-proton elastic scattering cross section ratio, R2γ, over a wide range of the virtual photon polarization, 0.456 < ε < 0.978. This provides a direct measure of hard two-photon exchange in elastic lepton-proton scattering widely thought to explain the discrepancy observed between unpolarized and polarized measurements of the proton form factor ratio, . The OLYMPUS results are small, within 1% on unity, over the range of momentum transfers measured and significantly lower than theoretical calculations that can explain part of the observed discrepancy in terms of two-photon exchange at higher momentum transfers. However, the results are in reasonable agreement with predictions based on phenomenological fits to the available form factor data.The motivation for measuring R2γ will be presented followed by a description of the OLYMPUS experiment. The importance of radiative corrections in the analysis will be shown also. Then we will present the OLYMPUS results and compare with results from two similar experiments and theoretical calculations.

Proton radius from electron-proton scattering and chiral perturbation theory

We determine the root-mean-square proton charge radius, $R_{\rm p}$, from a fit to low-$Q^2$ electron-proton elastic scattering cross section data with the higher moments fixed (within uncertainties) to the values predicted by chiral perturbation theory. We obtain $R_{\rm p}=0.857(11)$ fm. This number falls between the value obtained from muonic hydrogen analyses and the CODATA value (based upon atomic hydrogen spectroscopy and electron-proton scattering determinations).

Evaluation of the strength of electron-proton scattering data for determining the proton charge radius

Precisely measured electron-proton elastic scattering cross sections [Phys. Rev. Lett. {\bf 105}, 242002 (2010)] are reanalyzed to evaluate their strength for determining the rms charge radius ($R_{\rm E}$) of the proton. More than half of the cross sections at lowest $Q^2$ are fit using two single-parameter form-factor models, with the first based on a dipole parametrization, and the second on a linear fit to a conformal-mapping variable. These low-$Q^2$ fits extrapolate the slope of the form factor to $Q^2$=0 and determine $R_{\rm E}$ values of approximately 0.84 and 0.89~fm, respectively. Fits spanning all $Q^2$, in which the single constants are replaced with cubic splines at larger $Q^2$, lead to similar results for $R_{\rm E}$. We conclude that the scattering data is consistent with $R_{\rm E}$ ranging from at least 0.84 to 0.89~fm, and therefore cannot resolve the discrepancy between determinations of $R_{\rm E}$ made using muonic and electronic hydrogen-atom spectroscopy.

Towards a resolution of the proton form factor problem: new electron and positron scattering data.

There is a significant discrepancy between the values of the proton electric form factor, G(E)(p), extracted using unpolarized and polarized electron scattering. Calculations predict that small two-photon exchange (TPE) contributions can significantly affect the extraction of G(E)(p) from the unpolarized electron-proton cross sections. We determined the TPE contribution by measuring the ratio of positron-proton to electron-proton elastic scattering cross sections using a simultaneous, tertiary electron-positron beam incident on a liquid hydrogen target and detecting the scattered particles in the Jefferson Lab CLAS detector. This novel technique allowed us to cover a wide range in virtual photon polarization (ϵ) and momentum transfer (Q(2)) simultaneously, as well as to cancel luminosity-related systematic errors. The cross section ratio increases with decreasing ϵ at Q(2)=1.45 GeV(2). This measurement is consistent with the size of the form factor discrepancy at Q(2)≈1.75 GeV(2) and with hadronic calculations including nucleon and Δ intermediate states, which have been shown to resolve the discrepancy up to 2-3 GeV(2).

EM Form Factors and OLYMPUS

The elastic form factors of the nucleon characterize the distributions of charge and magnetization in momentum space and are important input for calculations of strong interaction phenomena and nuclear structure. The dramatic discrepancy in the observed ratio of elastic proton form factors between the Rosenbluth separation and polarization transfer methods has invoked numerous theoretical and experimental investigations. The previously neglected effect from two-photon exchange has become the favored explana- tion for the discrepancy. While the effect can not be calculated from first principles, it can be verified experimentally in several ways, most stringently by comparing the positron- proton and electron-proton elastic cross sections. The OLYMPUS experiment at DESY has been carried out to quantify the effect of two-photon exchange using intense stored positron and electron beams along with an internal unpolarized hydrogen target and a large acceptance detector to measure the ratio of the positron-proton and electron-proton elastic scattering cross sections. The status of proton form factor measurements and of the experimental efforts to verify the effect of two-photon exchange is presented, with some emphasis on the OLYMPUS experiment.

Probing two-photon exchange with OLYMPUS

Two-photon exchange is believed to be responsible for the discrepancies in the proton electric to magnetic form factor ratio found with the Rosenbluth and polarization transfer methods. If this explanation is correct, one expects significant di erences in the lepton-proton cross sections between positrons and electrons. The OLYMPUS experi- ment at DESY in Hamburg, Germany was designed to measure the ratio of unpolarized positron-proton and electron-proton elastic scattering cross sections over a wide kine- matic range with high precision, in order to quantify the e ect of two-photon exchange. The experiment used intense beams of electrons and positrons stored in the DORIS ring at 2.0 GeV interacting with an internal windowless hydrogen gas target. The current status of OLYMPUS will be discussed.

Reexamination of phenomenological two-photon exchange corrections to the proton form factors ande±pscattering

We extract the two-photon exchange (TPE) contributions to electron--proton elastic scattering using two parametrizations and compare the results to different phenomenological extractions and direct calculations of the TPE effects. We find that many of the extractions give similar results, and highlight the common assumptions and the impact of not including such assumptions. We provide a simple parametrization of the TPE contribution to the unpolarized cross section, along with an estimate of the fit uncertainties and the uncertainties associated with the assumptions made in the extraction. We look at the contributions as extracted from various e--p elastic scattering observables, and make predictions for ratio $R^{e^{+} e^{-}}$ of positron-proton to electron-proton elastic scattering cross sections.

Erratum: Empirical parametrization of the two-photon-exchange effect contributions to the electron-proton elastic scattering cross section [Phys. Rev. C83, 054307 (2011)

Erratum: Empirical parametrization of the two-photon-exchange effect contributions to the electron-proton elastic scattering cross section [Phys. Rev. C<b>83</b>, 054307 (2011)

Empirical parametrization of the two-photon-exchange effect contributions to the electron-proton elastic scattering cross section

The most recent electron-proton elastic scattering data were re-analyzed using an empirical parametrization of the two-photon-exchange (TPE) effect contributions to ${\ensuremath{\sigma}}_{R}$. The TPE effect contribution $F({Q}^{2},\ensuremath{\varepsilon})$ was double Taylor series expanded as a polynomial of order $n$ keeping only terms linear in $\ensuremath{\varepsilon}$ to account for the experimentally observed and verified linearity of the Rosenbluth plots. We fix the ratio $R={G}_{\mathit{Ep}}/{G}_{\mathit{Mp}}$ to be that obtained from a fit to the recoil-polarization data and parametrize ${\ensuremath{\sigma}}_{R}$ first by a three-parameter formula (fit I) and then by a two-parameter formula (fit III). In contrast to previous analyses, the fit parameter ${G}_{\mathit{Mp}}^{2}$ as obtained from these fits is either smaller or equal to the values obtained from our conventional Rosenbluth fit (fit II) but never larger. The ratio $g({Q}^{2})/{G}_{\mathit{Mp}}^{2}$ which represents the ratio of the TPE and one-photon-exchange (OPE) effect contributions to the intercept of ${\ensuremath{\sigma}}_{R}$ is large and it ranges 3%$\ensuremath{-}$88%. The ratio ${R}_{1\ensuremath{\gamma}\ensuremath{\bigotimes}2\ensuremath{\gamma}}=\ensuremath{\tau}f({Q}^{2})/{G}_{\mathit{Ep}}^{2}$ which represents the ratio of the TPE and OPE effect contributions to the slope of ${\ensuremath{\sigma}}_{R}$ is also large, reaching a value of 12.0$\ensuremath{-}$14.4 at ${Q}^{2}=$ 5.25 (GeV/c)${}^{2}$. The ratio ${R}_{1\ensuremath{\gamma}\ensuremath{\bigotimes}2\ensuremath{\gamma}}$ as obtained from fits I and III is consistent, within error, with those obtained from previous analyses. Our formulas seem to explain the linearity of ${\ensuremath{\sigma}}_{R}$. Moreover, our analysis shows that the extracted ${G}_{\mathit{Ep}}^{2}$ and ${G}_{\mathit{Mp}}^{2}$ using the conventional Rosenbluth separation method can in fact be broken into the usual OPE and TPE contributions. Therefore, ${\ensuremath{\sigma}}_{R}$ can in fact be derived under weaker conditions than those imposed by the Born approximation. Our results show that the TPE amplitudes, $g({Q}^{2})/{G}_{\mathit{Mp}}^{2}$ and $f({Q}^{2})/{G}_{\mathit{Mp}}^{2}$, are sizable and grow with ${Q}^{2}$ value up to ${Q}^{2}~$ 6 (GeV/c)${}^{2}$ in agreement with previous studies. A revision of and comparison to previous analyses are also presented.

Is there model-independent evidence of the two-photon-exchange effect in the electron–proton elastic scattering cross section?

We re-analyze the data of the elastic electron proton scattering to look for model-independent evidence of the two-photon-exchange (TPE) effect. In contrast to previous analyses, TPE effect is parametrized in forms which are free of kinematical-singularity, in addition to being consistent with the constraint derived from crossing symmetry and the charge conjugation. Moreover, we fix the value of R=GE/GM as determined from the data of the polarization transfer experiment. We find that, at high Q2⩾2 GeV2 values, the contribution of the TPE effect to the slope of σR vs. ε is large and comparable with that arising from GE. It also behaves quasi-linearly in the region of current data, namely, in the range of 0.2<ε<0.95. Hence the fact that the current elastic ep cross section data shows little nonlinearity with respect to ε cannot be used to exclude the presence of the TPE effect. More precise data at extreme angles will be crucial for a model-independent extraction of the TPE effect.

Evidence for two-photon exchange contributions in electron-proton and positron-proton elastic scattering

The comparison of positron-proton and electron-proton elastic scattering cross sections is a sensitive test for the presence of two-photon exchange contributions. Thirty years ago, positron data were considered adequate to set tight limits on the size of two-photon corrections. More recently, these radiative corrections have again become a matter of great interest as a possible explanation for the discrepancy between Rosenbluth and polarization transfer measurements of the proton electromagnetic form factors. We have reexamined the electron and positron scattering data to see if they can accommodate two-photon effects of the size necessary to account for the Rosenbluth-polarization transfer discrepancy. The data are consistent with simple estimates of the two-photon contributions necessary to explain the discrepancy. In fact, they strongly favor a large epsilon-dependent correction to the positron to electron ratio, providing the first direct experimental evidence for a two-photon contribution to unpolarized lepton-proton scattering.

Electromagnetic form factors of the peoton at low four-momentum transfer (II)

The 300 MeV electron linear accelerator of Mainz has been used to measure the angular dependence of the electron-proton elastic scattering cross sections at seven different energies for squared four-momentum transfers between 0.13 and 4.7 fm −2. The proton form factors have been extracted from the cross sections by means of Rosenbluth plots and by fitting parametrized analytical functions directly to the cross sections. The best fit is compared to the data of other laboratories. The previously reported deviations from the dipole fit have been confirmed. From the form factors at q 2<0.9 fm 2 the proton r.m.s. radius has been determined. A determination of the spectral function of the nucleon isovector form factor G E V in the time-like is obtained using a realistic ϱ resonance.

Proton form factor from 0.15 to 0.79fm−2

The absolute electron-proton elastic scattering cross section has been measured by detecting the recoil protons. The proton charge form factor has been extracted for values of the square of the momentum transfer between 0.15 and 0.79 fm−2. The rms charge radius determined from these measurements is 0.81±0.04 fm. [NUCLEAR REACTIONS H1(e,p), E=55−130 MeV, measured σ(E;Ep,θ); deduced charge form factor, rms charge radius.]

Electromagnetic form factors of the proton at low four-momentum transfer

Electron-proton elastic scattering cross sections were measured at low four-momentum transfers squared ( q 2 from 0.13 to 2.15 fm −2) at six different energies between 150 and 275 MeV. The electric ( G E) and magnetic ( G M) form factors of the proton have been determined by Rosenbluth plots and independently by using analytical functions for the form factors to fit the cross sections. The electric form factor is found to deviate significantly from the dipole fit. From the slope of the form factor functions at q 2 = 0 the rms radii of the charge and the magnetic moment distribution were determined. The charge rms radius is found to be more than 10% larger than the value given by the dipole fit.

Measurement of proton and neutron electromagnetic form factors at squared four-momentum transfers up to 3 (GeV/c) 2

Electron-proton elastic scattering cross sections have been measured at squared four-momentum transfers q 2 of 0.67, 1.00, 1.17, 1.50, 1.75, 2.33 and 3.00 (GeV/ c) 2 and Electron scattering angles θ e between 10° and 20° and at about 86° in the laboratory. The proton electromagnetic form factors G E p and G M p were determined. The results indicate that G E p ( q 2) decreases faster with increasing q 2 than G M p ( q 2). Quasi-elastic electron-deuteron cross sections have been determined at values of q 2 = 0.39, 0.565, 0.78, 1.0 and 1.5 (GeV/ c) 2 and scattering angles between 10° and 12°. At q 2 = 0.565 (GeV/ c 2 data have also been taken with θ e = 35° and at q 2 = 1.0 and 1.5 (GeV/ c) 2 with θ e = 86°. Electron-proton as well as electron-neutron scattering cross sections have been deduced by the ratio method. The theoretical uncertainties of this procedure are shown to be small by comparison of the bound with the free proton cross sections. The magnetic form factor of the neutron G M n derived from the data is consistent with the scaling law. The charge form factor of the neutron is found to be small.

Elastic Electron-Proton Scattering at Large Four-Momentum Transfer

Electron-proton elastic-scattering cross sections have been measured at the Stanford Linear Accelerator Center for four-momentum transfers squared q^2 from 1.0 to 25.0 (GeV/c)^2. The electric (GEp) and magnetic (GMp) form factors of the proton were not separated, since angular distributions were not measured at each q^2. However, values for GMp were derived assuming various relations between GEp and GMp. Several theoretical models for the behavior of the proton magnetic form factor at high values of q^2 are compared with the data.