Proton Form Factor Ratio Research Articles

Proton form factor ratio μpGEp/GMp from double spin asymmetry

The ratio of the electric and magnetic form factor of the proton, $\mu_p G_E^p/G_M^p$, has been measured for elastic electron-proton scattering with polarized beam and target up to four-momentum transfer squared, $Q^2=5.66$ (GeV/c)$^2$ using the double spin asymmetry for target spin orientation aligned nearly perpendicular to the beam momentum direction. This measurement of $\mu_p G_E^p/G_M^p$ agrees with the $Q^2$ dependence of previous recoil polarization data and reconfirms the discrepancy at high $Q^2$ between the Rosenbluth and the polarization-transfer method with a different measurement technique and systematic uncertainties uncorrelated to those of the recoil-polarization measurements. The form factor ratio at $Q^2$=2.06 (GeV/c)$^2$ has been measured as $\mu_p G_E^p/G_M^p = 0.720 \pm 0.176_{stat} \pm 0.039_{sys}$, which is in agreement with an earlier measurement with the polarized target technique at similar kinematics. The form factor ratio at $Q^2$=5.66 (GeV/c)$^2$ has been determined as $\mu_p G_E^p/G_M^p=0.244\pm0.353_{stat}\pm0.013_{sys}$, which represents the highest $Q^2$ reach with the double spin asymmetry with polarized target to date.

Quasi-elastic polarization-transfer measurements on the deuteron in anti-parallel kinematics

We present measurements of the polarization-transfer components in the H2(e→,e′p→) reaction, covering a previously unexplored kinematic region with large positive (anti-parallel) missing momentum, pmiss, up to 220MeV/c, and Q2=0.65(GeV/c)2. These measurements, performed at the Mainz Microtron (MAMI), were motivated by theoretical calculations which predict small final-state interaction (FSI) effects in these kinematics, making them favorable for searching for medium modifications of bound nucleons in nuclei. We find in this kinematic region that the measured polarization-transfer components Px and Pz and their ratio agree with the theoretical calculations, which use free-proton form factors. Using this, we establish upper limits on possible medium effects that modify the bound proton's form factor ratio GE/GM at the level of a few percent. We also compare the measured polarization-transfer components and their ratio for 2H to those of a free (moving) proton. We find that the universal behavior of 2H, 4He and 12C in the double ratio (Px/Pz)A(Px/Pz)H1 is maintained in the positive missing-momentum region.

Study of the process e+e−→pp¯ via initial state radiation at BESIII

The Born cross section for the process $e^+ e^- \to p \bar p $ is measured using the initial state radiation technique with an undetected photon. This analysis is based on datasets corresponding to an integrated luminosity of 7.5 fb$^{-1}$, collected with the BESIII detector at the BEPCII collider at center of mass energies between 3.773 and 4.600 GeV. The Born cross section for the process $e^+ e^- \to p \bar p $ and the proton effective form factor are determined in the $p\bar p$ invariant mass range between 2.0 and 3.8 GeV/$c^2$ divided into 30 intervals. The proton form factor ratio ($|G_E|/|G_M|$) is measured in 3 intervals of the $p\bar p$ invariant mass between 2.0 and 3.0 GeV/$c^2$.

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.

Polarization transfer observables in elastic electron-proton scattering at Q2=2.5 , 5.2, 6.8, and 8.5 GeV2

The GEp-III and GEp-2$\gamma$ experiments were carried out in Jefferson Lab's (JLab's) Hall C from 2007-2008, to extend the knowledge of $G_E^p/G_M^p$ to the highest practically achievable $Q^2$ and to search for effects beyond the Born approximation in polarization transfer observables of elastic $\vec{e}p$ scattering. This article reports an expanded description of the common experimental apparatus and data analysis procedure, and the results of a final reanalysis of the data from both experiments, including the previously unpublished results of the full-acceptance data of the GEp-2$\gamma$ experiment. The Hall C High Momentum Spectrometer detected and measured the polarization of protons recoiling elastically from collisions of JLab's polarized electron beam with a liquid hydrogen target. A large-acceptance electromagnetic calorimeter detected the elastically scattered electrons in coincidence to suppress inelastic backgrounds. The final GEp-III data are largely unchanged relative to the originally published results. The statistical uncertainties of the final GEp-2$\gamma$ data are significantly reduced at $\epsilon = 0.632$ and $0.783$ relative to the original publication. The decrease with $Q^2$ of $G_E^p/G_M^p$ continues to $Q^2 = 8.5$ GeV$^2$, but at a slowing rate relative to the approximately linear decrease observed in earlier Hall A measurements. At $Q^2 = 2.5$ GeV$^2$, the proton form factor ratio $G_E^p/G_M^p$ shows no statistically significant $\epsilon$-dependence, as expected in the Born approximation. The ratio $P_\ell/P_\ell^{Born}$ of the longitudinal polarization transfer component to its Born value shows an enhancement of roughly 1.4\% at $\epsilon = 0.783$ relative to $\epsilon = 0.149$, with $\approx 1.9\sigma$ significance based on the total uncertainty, implying a similar effect in the transverse component $P_t$ that cancels in the ratio $R$.

Two-photon exchange amplitude withπNintermediate states: Spin-1/2 and spin-3/2 channels

We calculate two-photon exchange (TPE) amplitudes for the elastic electron-proton scattering, and take into account intermediate hadronic states containing \pi N system with total angular momentum 1/2 or 3/2, which includes 8 different channels. This is the improvement of our previous calculation, where only the \pi N states with quantum numbers of \Delta(1232) resonance were included. The results show good consistency with recent experimental data. At high Q^2, newly-calculated contributions affect the correction to the measured proton form factor ratio \mu G_E/G_M. The total correction becomes somewhat smaller compared to our previous work, but is still significant and grows approximately linearly with Q^2. Comparing contributions of different channels, we found that larger contributions come from the channels with quantum numbers of lightest resonances.

The structure of the nucleon: Elastic electromagnetic form factors

Precise proton and neutron form factor measurements at Jefferson Lab, using spin observables, have recently made a significant contribution to the unraveling of the internal structure of the nucleon. Accurate experimental measurements of the nucleon form factors are a test-bed for understanding how the nucleon’s static properties and dynamical behavior emerge from QCD, the theory of the strong interactions between quarks. There has been enormous theoretical progress, since the publication of the Jefferson Lab proton form factor ratio data, aiming at reevaluating the picture of the nucleon. We will review the experimental and theoretical developments in this field and discuss the outlook for the future.

Radiative corrections to polarization observables in electron-proton scattering

We consider radiative corrections to polarization observables in elastic electron-proton scattering, in particular, for the polarization transfer measurements of the proton form factor ratio $\mu G_E/G_M$. The corrections are of two types: two-photon exchange (TPE) and bremsstrahlung (BS); in the present work we pay special attention to the latter. Assuming small missing energy or missing mass cut-off, the correction can be represented in a model-independent form, with both electron and proton radiation taken into account. Numerical calculations show that the contribution of the proton radiation is not negligible. Overall, at high $Q^2$ and energies the total correction to $\mu G_E/G_M$ grows, but is dominated by TPE. At low energies both TPE and BS may be significant; the latter amounts to ~ 0.01 for some reasonable cut-off choices.

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.

The Proton Form Factor Ratio Measurements at Jefferson Lab

The ratio of the proton form factors, GEp/GMp, has been measured from Q2 of 0.5 GeV2 to 8.5 GeV2, at the Jefferson Laboratory, using the polarization transfer method. This ratio is extracted directly from the measured ratio of the transverse and longitudinal polarization components of the recoiling proton in elastic electron-proton scattering. The discovery that the proton form factor ratio measured in these experiments decreases approximately linearly with four-momentum transfer, Q2, for values above ? 1 GeV2, is one of the most significant results to come out of JLab. These results have had a large impact on progress in hadronic physics; and have required a significant rethinking of nucleon structure. The increasingly common use of the double-polarization technique to measure the nucleon form factors, in the last 15 years, has resulted in a dramatic improvement of the quality of all four nucleon electromagnetic form factors, GEp, GMp, GEn and GMn. There is an approved experiment at JLab, GEP(V), to continue the ratio measurements to 12 GeV2. A dedicated experimental setup, the Super Bigbite Spectrometer (SBS), will be built for this purpose. It will be equipped with a focal plane polarimeter to measure the polarization of the recoil protons. The scattered electrons will be detected in an electromagnetic calorimeter. In this presentation, I will review the status of the proton elastic electromagnetic form factors and discuss a number of theoretical approaches to describe nucleon form factors.

The proton form factor measurements at Jefferson Lab, past and future

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.

The OLYMPUS experiment

The OLYMPUS experiment was designed to measure the ratio between the positron–proton and electron–proton elastic scattering cross-sections, with the goal of determining the contribution of two-photon exchange to the elastic cross-section. Two-photon exchange might resolve the discrepancy between measurements of the proton form factor ratio, μpGEp/GMp, made using polarization techniques and those made in unpolarized experiments. OLYMPUS operated on the DORIS storage ring at DESY, alternating between 2.01GeV electron and positron beams incident on an internal hydrogen gas target. The experiment used a toroidal magnetic spectrometer instrumented with drift chambers and time-of-flight detectors to measure rates for elastic scattering over the polar angular range of approximately 25°–75°. Symmetric Møller/Bhabha calorimeters at 1.29° and telescopes of GEM and MWPC detectors at 12° served as luminosity monitors. A total luminosity of approximately 4.5fb−1 was collected over two running periods in 2012. This paper provides details on the accelerator, target, detectors, and operation of the experiment.

Final analysis of proton form factor ratio data atQ2=4.0, 4.8, and 5.6 GeV2

Precise measurements of the proton electromagnetic form factor ratio $R = \mu_p G_E^p/G_M^p$ using the polarization transfer method at Jefferson Lab have revolutionized the understanding of nucleon structure by revealing the strong decrease of $R$ with momentum transfer $Q^2$ for $Q^2 \gtrsim 1$ GeV$^2$, in strong disagreement with previous extractions of $R$ from cross section measurements. In particular, the polarization transfer results have exposed the limits of applicability of the one-photon-exchange approximation and highlighted the role of quark orbital angular momentum in the nucleon structure. The GEp-II experiment in Jefferson Lab's Hall A measured $R$ at four $Q^2$ values in the range 3.5 GeV$^2 \le Q^2 \le 5.6$ GeV$^2$. A possible discrepancy between the originally published GEp-II results and more recent measurements at higher $Q^2$ motivated a new analysis of the GEp-II data. This article presents the final results of the GEp-II experiment, including details of the new analysis, an expanded description of the apparatus and an overview of theoretical progress since the original publication. The key result of the final analysis is a systematic increase in the results for $R$, improving the consistency of the polarization transfer data in the high-$Q^2$ region. This increase is the result of an improved selection of elastic events which largely removes the systematic effect of the inelastic contamination, underestimated by the original analysis.

THE PROTON FORM FACTOR RATIO AT LOW Q2: NEW RESULTS FROM JEFFERSON LAB

Recently an experiment at Jefferson Lab has measured the proton form factor ratio, [Formula: see text], down to Q2 ~ 0.3 GeV 2 with unprecedented precision. Based on the results from this experiment, a re-analysis was carried out for the world data on proton form factors, and a new result was extracted for the proton charge radius. The new result is consistent with published CODATA results and is at odds with the new muonic hydrogen measurement at PSI. We present the results of the new measurement, as well as discuss an upcoming experiment to measure the form factor ratio down to even lower Q2.

New Measurements of the Proton Electromagnetic Form Factor Ratio at Low [formula omitted

Polarization measurements are allowing the electric to magnetic form factor ratio of the proton to be determined with unprecedented precision. Recent results indicate that there is a large deviation from unity in the proton form factor ratio around Q 2 ≃ 0.35 GeV 2 . Furthermore, the deviation from unity is attributed to a deviation of the electric form factor from standard fits and calculations. A new, partially completed, experiment will significantly improve the existing data and will determine the presence, if any, of a narrow structure in the form factor ratio. The new measurement, combined with the expected high precision cross section measurements, will allow the extraction of individual form factors with unprecedented accuracy at low Q 2 .

New Proton Form Factor Ratio Recoil Polarization Measurements in Hall C at JLab

The experimental determination of the proton elastic form factors has become a very active field since two experiments at JLab using the double-polarization technique revealed a stark discrepancy from the previous Rosenbluth data. In a next step, started in the fall of 2007, a new experiment in Hall C at JLab has pushed the Q 2 limit from 5.6 to 8.54 GeV 2 , with intermediate points at 5.2 and 6.8 GeV 2 . The kinematics dependence of the form factor ratio at 2.5 GeV 2 has also been investigated. The current status of the data analysis and some preliminary results are reported.

THE BLAST EXPERIMENT: POLARIZED ELECTRON SCATTERING FROM HYDROGEN AND DEUTERIUM

At the MIT-Bates Linear Accelerator Center, the nucleon form factors have been measured by scattering polarized electrons from vector-polarized hydrogen and deuterium. The experiment used the longitudinally polarized electron beam stored in the MIT-Bates South Hall Ring along with an isotopically pure, highly vector-polarized internal atomic hydrogen and deuterium target provided by an atomic beam source. The measurements were carried out with the symmetric Bates Large Acceptance Spectrometer Toroid (BLAST). Results are presented for the proton form factor ratio, [Formula: see text], and for the charge form factor of the neutron, [Formula: see text]. Both results are more precise than previous data in the corresponding Q2 ranges.

Phenomenological analysis of two-photon exchange effects in proton form factor measurements

We perform a model-independent phenomenological analysis of experimental data on proton form factor ratio. We find that only one of the two-photon exchange amplitudes, which we call $\ensuremath{\delta}{\mathcal{G}}_{M}$, is responsible for the discrepancy between Rosenbluth and polarization methods. The linearity of Rosenbluth plots implies that $\ensuremath{\delta}{\mathcal{G}}_{M}$ is approximately linear function of \ensuremath{\varepsilon}. The slope of $\ensuremath{\delta}{\mathcal{G}}_{M}$ is extracted from experimental data and is shown to be consistent with theoretical calculations.

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 $Q^2$.

The ratio of the magnetic to the electric proton form factors in Quantum Chromodynamics

We propose a two parameter expression for the high momentum transfer behaviour of the ratio of proton form factors G M( Q 2)/ Q E( Q 2) based on perturbation theory calculations in Quantum Chromodynamics. A fit to the present experimental data and its consistency with a previous fit to the high Q 2 behaviour of the Dirac form factor [1] is also discussed.