Proton Form Factors Research Articles

Prediction of rms charge radius of proton using proton-proton elastic scattering data at TeV

Using proton–proton elastic scattering data at TeV and squared four-momentum transfer 0.36 < -t < 0.76 (GeV/c)2 for 13 σBeam distance and 0.07 < -t < 0.46 (GeV/c)2 for 4.3 σBeam distance, form factor of proton is predicted. Simplest version of Chou–Yang model is employed to extract the form factor by fitting experimental data of differential cross section from TOTEM experiment (for 13σBeamand 4.3 σBeam distance) to a single Gaussian. Root mean square (rms) charge radius of proton is calculated using this form factor. It is found to be equal to 0.91 fm and 0.90 fm respectively. Which is in good agreement with experimental data and theoretically predicted values.

New fit of timelike proton electromagnetic formfactors from e+e− colliders

The data on the proton form factors in the time-like region from the BaBar, BESIII and CMD-3 Collaborations are examined to have coherent pieces of information on the proton structure. Oscillations in the annihilation cross section, previously observed, are determined with better precision. The moduli of the individual form factors, determined for the first time, their ratio and the angular asymmetry of the annihilation reaction $e^+e^-\to\bar p p$ are discussed. Fiits of the available data on the cross section, the effective form factor, and the form factor ratio, allow to propose a description of the electric and magnetic time-like form factors from the threshold up to the highest momenta.

Two-Photon Exchange in Elastic Electron Scattering on Hadronic Systems

In the present review, we discuss different aspects of the two-photon exchange (TPE) physics in elastic ep scattering at high Q2, as well as at low Q2. The imaginary part of the TPE amplitude gives rise to beam and target single-spin asymmetries. Different theoretical approaches to the calculation of these observables are considered. The real part of the TPE amplitude influences the unpolarized cross-section and double-spin observables and is, most likely, responsible for the discrepancy between two methods of measurements of the proton form factors. We review different methods of calculations of the TPE amplitudes in the framework of the “hadron” and “quark-gluon” approaches. We discuss the dispersion approach suitable for low and intermediate Q2, which includes elastic and inelastic intermediate hadronic states, as well as the connection of TPE with the proton radius puzzle. The present situation with direct experimental searches for the TPE amplitude in the e+p/e−p charge asymmetry is also discussed, as well as attempts to extract the TPE amplitudes from existing experimental data obtained by the Rosenbluth and double polarization techniques. The TPE physics in other processes such as elastic мp, e-nucleus, and еп scattering is also reviewed.

Proton Electromagnetic Form Factors Data Are in Disagreement with New Electron-Positron Annihilation into Proton-Antiproton Pair Total Cross Section Measurements

In this paper a consistency of new very precise data on electron-positron annihilation into proton-antiproton pair total cross section with existing proton and neutron electromagnetic form factors data is investigated. First, the result is represented by a theoretically predicted dashed line for the total cross section obtained in the simultaneous analysis of the proton and neutron form factors data by the advanced nucleon electromagnetic structure Unitary and Analytic model, and then, as the neutron data are always less precise from objective reasons than the proton data, the result is also represented by a theoretically predicted full line for the total cross section obtained in the analysis of only the proton form factors data in space-like and time-like regions by the advanced proton electromagnetic structure Unitary and Analytic model. In both cases one finds disagreement between the electron-positron annihilation into proton-antiproton pair total cross section data and the corresponding form factors data, which is demonstrated by a disagreement of the dashed and full curves representing theoretically predicted electron-positron annihilation into proton-antiproton pair total cross sections behaviors.

Parametrization and applications of the low- Q2 nucleon vector form factors

We present the proton and neutron vector form factors in a convenient parametric form that is optimized for momentum transfers $\lesssim$ few GeV$^2$. The form factors are determined from a global fit to electron scattering data and precise charge radius measurements. A new treatment of radiative corrections is applied. This parametric representation of the form factors, uncertainties and correlations provides an efficient means to evaluate many derived observables. We consider two classes of illustrative examples: neutrino-nucleon scattering cross sections at GeV energies for neutrino oscillation experiments and nucleon structure corrections for atomic spectroscopy. The neutrino-nucleon charged current quasielastic (CCQE) cross section differs by 3-5% compared to commonly used form factor models when the vector form factors are constrained by recent high-statistics electron-proton scattering data from the A1 Collaboration. Nucleon structure parameter determinations include: the magnetic and Zemach radii of the proton and neutron, $[r_M^p, r_M^n] = [ 0.739(41)(23), 0.776(53)(28)]$ fm and $[r_Z^p, r_Z^n] = [ 1.0227(94)(51), -0.0445(14)(3)]$ fm; the Friar radius of nucleons, $[(r^p_F)^3, (r^n_F)^3] = [2.246(58)(2), 0.0093(6)(1)]$ fm$^3$; the electric curvatures, $[\langle r^4 \rangle^p_E, \langle r^4 \rangle^n_E ] = [1.08(28)(5), -0.33(24)(3)]$ fm$^4$; and bounds on the magnetic curvatures, $[ \langle r^4 \rangle^p_M, \langle r^4 \rangle^n_M ] = [ -2.0(1.7)(0.8), -2.3(2.1)(1.1)]$ fm$^4$. The first and dominant uncertainty is propagated from the experimental data and radiative corrections, and the second error is due to the fitting procedure.

Form Factor of Proton Predicted Using the Data of ppbar Elastic Scattering at $$\boldsymbol{\sqrt{s}=1.96}$$ eV

Based on the behavior of elastic scattering of proton and anti-proton at $$\sqrt{s}=1.96$$ TeV for squared four-momentum transfer $$0.26<{-}t<1.2($$ GeV $$/c)^{2}$$ , form factor of proton is predicted. Simplest version of Chou–Yang model is employed for extracting this form factor by fitting experimental data of differential cross section from D0 experiment to a single Gaussian. Root mean square (rms) matter radius of proton is calculated using this form factor. It is found to be equal to 0.89 fm. Which is in good agreement with experimental data and theoretically predicted values from other models.

Effects of finite nucleon size, vacuum polarization, and electromagnetic spin-orbit interaction on nuclear binding energies and radii in spherical nuclei

The electromagnetic effects of the finite size of the nucleon are implemented self-consistently on top of the Skyrme Hartree-Fock calculation, where the electric form factors of both protons and neutrons are considered. Furthermore, the vacuum polarization and the electromagnetic spin-orbit interaction are taken into account. The self-consistent finite-size effects give a different Coulomb potential from the conventional one and affect the neutrons as well. The contribution of the finite-size effects to the total energy reaches $ 7 \, \mathrm{MeV} $ in $ {}^{208} \mathrm{Pb} $. The vacuum polarization and the electromagnetic spin-orbit interaction are also non-negligible, especially in the heavy nuclei. These effects provide a comparable contribution of the total energy to that of the isospin symmetry-breaking terms of the nuclear interaction. The mirror nuclei mass difference in $ {}^{48} \mathrm{Ca} $--$ {}^{48} \mathrm{Ni} $ is also studied, and its value is improved by approximately one order of magnitude.

How much two-photon exchange is needed to resolve the proton form factor discrepancy?

One possible explanation for the proton form factor discrepancy is a contribution to the elastic electron–proton cross section from hard two-photon exchange (TPE), a typically neglected radiative correction. Hard TPE cannot be calculated in a model-independent way, but it can be determined experimentally by looking for deviations from unity in the ratio of positron-proton to electron–proton cross sections. Three recent experiments have measured this cross section ratio to quantify hard TPE. To interpret the results of these experiments, it is germane to ask: ‘How large of a deviation from unity is necessary to fully resolve the form factor discrepancy?’ With a minimal set of assumptions and using global fits to unpolarized and polarized elastic scattering data, I estimate the necessary size of the TPE correction in the kinematics of the three recent experiments and compare to their measurements. I find wide variation when using different global fits, implying that the magnitude of the form factor discrepancy is not well-constrained. The recent hard TPE measurements can easily accommodate the hypothesis that TPE underlies the proton form factor discrepancy.

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.

Recent highlights with baryons from lattice QCD

Highlights from recent computations in lattice QCD involving baryons are presented. Calcula tions of the proton mass and spin decompositions are discussed, a percent level determination of the nucleon axial coupling is described, and determinations of the proton and neutron electromagnetic form factors and light-cone parton distribution functions are outlined. Recent results applying the so-called Luscher method to meson-baryon systems are presented. Key points emphasized are that much better precision with disconnected diagrams is being achieved, incorporating multi-hadron operators is now feasible, and more and more studies are being done with physical quark masses.

Proton and Neutron Electromagnetic Form Factors Based on Bound System in 3 + 1 Dimensional QCD

We propose a new description of a nucleon as a pair of pions. The baryon number of our description of nucleon is not 1 but 0. However, this is probable because the proton spin crisis shows that the baryon spin cannot tell the number of composing quarks anymore. Because we use the derived pion wave function to describe a nucleon, our description has automatically the pionic degree of freedom and can be compared to the constituent quark model. Using this description, we investigate the electric charge and magnetization density functions of protons and neutrons. The electric charge density function of neutron is quite similar to those of Galster model and Maints data except the magnitude of singularity. The density functions of proton also show the similar behavior as those of Kelly’s except near origin. Taking the Fourier transform of the density functions, we obtain the Sachs electromagnetic form factors that can be compared to those in the parametrization derived by Ye et al.

Proton and neutron electromagnetic form factors from lattice QCD

The electromagnetic form factors of the proton and the neutron are computed within lattice QCD using simulations with quarks masses fixed to their physical values. Both connected and disconnected contributions are computed. We analyze two new ensembles of $N_f = 2$ and $N_f = 2 + 1 + 1$ twisted mass clover-improved fermions and determine the proton and neutron form factors, the electric and magnetic radii, and the magnetic moments. We use several values of the sink-source time separation in the range of 1.0 fm to 1.6 fm to ensure ground state identification. Disconnected contributions are calculated to an unprecedented accuracy at the physical point. Although they constitute a small correction, they are non-negligible and contribute up to 15% for the case of the neutron electric charge radius.

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/$c^2$.

On the Double Spin Asymmetries in the Elastic Scattering of Electrons off Protons

Based on the obtained differential cross sections for the scattering of longitudinally polarized electrons, taking into account the polarization of the proton target or the longitudinal polarization of the recoil protons, the next single spin asymmetries are studied: breaking T-parity asymmetry in the spin of the target proton $${{A}^{{( \bot )}}}$$ , and the degree of longitudinal polarization of recoil protons $${{P}_{p}}$$ . Double spin asymmetries are also obtained and analyzed: asymmetry $${{A}_{{ep}}}$$ with respect to the correlation of the incident electron helicity and the spin of the target proton, and right-left asymmetry $${{D}_{p}}$$ of the degree of longitudinal polarization of the recoil proton. It is shown that these asymmetries make it possible to measure the ratios of the proton form factors $${{{{G}_{{Ep}}}} \mathord{\left/ {\vphantom {{{{G}_{{Ep}}}} {{{G}_{{Mp}}}}}} \right. \kern-0em} {{{G}_{{Mp}}}}}$$ and $${{{{G}_{{Mp}}}} \mathord{\left/ {\vphantom {{{{G}_{{Mp}}}} {{{G}_{{1p}}}}}} \right. \kern-0em} {{{G}_{{1p}}}}}$$ .

Density distributions, form factors and reaction cross sections for exotic 11Be and 15C nuclei

The ground state proton, neutron and matter densities of exotic 11Be and 15C nuclei are studied by means of the TFSM and BCM. In TFSM, the calculations are based on using different model spaces for the core and the valence (halo) neutron. Besides single particle harmonic oscillator wave functions are employed with two different size parameters Bc and Bv. In BCM, the halo nucleus is considered as a composite projectile consisting of core and valence clusters bounded in a state of relative motion. The internal densities of the clusters are described by single particle Gaussian wave functions.&#x0D; Elastic electron scattering proton form factors for these exotic nuclei are analyzed via the plane wave born approximation (PWBA). As the calculations in the BCM do not distinguish between protons and neutrons, the calculations of the proton form factors are restricted only by the TFSM.&#x0D; The reaction cross sections for these exotic nuclei are studied by means of the Glauber model with an optical limit approximation using the ground state densities of the projectile and target, where these densities are described by single Gaussian functions. The calculated reaction cross sections at high energy are in agreement with the experimental data.

Elastic electron scattering from 17Ne and 27P exotic nuclei

The ground state proton, neutron and matter densities andcorresponding root mean square radii of unstable proton-rich 17Neand 27P exotic nuclei are studied via the framework of the twofrequencyshell model. The single particle harmonic oscillator wavefunctions are used in this model with two different oscillator sizeparameters core b and halo , b the former for the core (inner) orbitswhereas the latter for the halo (outer) orbits. Shell model calculationsfor core nucleons and for outer (halo) nucleons in exotic nuclei areperformed individually via the computer code OXBASH. Halostructure of 17Ne and 27P nuclei is confirmed. It is found that thestructure of 17Ne and 27P nuclei have 25 / 2 (1d ) and 1/ 2 2s -dominantconfigurations, respectively. Elastic electron scattering form factorsof these exotic nuclei are also studied using the plane wave Bornapproximation. Effects of the long tail behavior of the proton densitydistribution on the proton form factors of 17Ne and 27P areanalyzed. It is found that the difference between the proton formfactor of 17Ne and that of stable 20Ne (or of 27P and that of stable31P) comes from the difference in the proton density distribution ofthe last two protons (or of the last proton) in the two nuclei. It isconcluded that elastic electron scattering will be an efficient tool (inthe near future) to examine proton-halo phenomena of proton-richnuclei.

Radiative corrections to elastic-electron proton scattering and uncertainty in proton charge radius

Higher-order QED radiative corrections to elastic electron-proton scattering are discussed. It is shown that they are relevant for high-precision experiments on proton form factor measurements. Analytic result are obtained for next-to-leading second order corrections to the electron line. Light pair corrections are taken into account. The role of the hadronic contribution to vacuum polarization is discussed. Numerical results are given for the conditions of the experiment on proton form factors performed by A1 Collaboration. Preliminary results are also shown for the set-up with reconstruction of momentum transfer from the recoil proton momentum.

Critical analysis of recent results on electron and positron elastic scattering on proton

Recent data on the cross section ratio for electron and positron elastic scattering on protons are discussed. A deviation from unity of this ratio constitutes a model independent signature of charge-odd contributions that arise from mechanisms beyond the one-photon approximation, as the exchange of two photons. The relevance of this issue is related to that fact that the information on the proton structure from lepton elastic (and inelastic) scattering holds only within a formalism based on the one photon exchange approximation. The present analysis shows that the deviations of the data from unity and from a previously developed theoretical approach lie within the theoretical and experimental errors. The data suggest that other reasons for explanation of the discrepancy between the electromagnetic proton form factors extracted from the experiments according to the polarized and the unpolarized methods are more likely.

BESIII results on time-like baryon form factors

This contribution reports on the recent measurements of baryon electromagnetic form factors at the BESIII experiment in Beijing. The Beijing e+e − collider BEPCII is a double-ring symmetric collider running at $ \sqrt s $ between 2.0 and 4.6 GeV. Baryon electromagnetic form factors can be measured at BESIII in direct e+e−-annihilation and in initial state radiation processes. Based on the data collected by the BESIII detector at 12 center of mass energies between 2.23 and 3.67 GeV, the measured $ \mathop e\nolimits^ + \mathop e\nolimits^ - \to \mathop p\limits^ - p $ cross section and the time-like proton form factor are presented. Preliminary results from the analysis of the initial state radiation process $ \mathop e\nolimits^ + \mathop e\nolimits^ - \to \mathop p\limits^ - p\gamma $ using a data set of 7.408 fb−1 collected at center of mass energies between 3.773 and 4.6 GeV, are also shown. The cross sections for $ \mathop e\nolimits^ + \mathop e\nolimits^ - \to \mathop {\mathop \Lambda \nolimits_c^ - }\limits^ - \mathop \Lambda \nolimits_c^ + $ and $ \mathop e\nolimits^ + \mathop e\nolimits^ - \to \mathop \Lambda \limits^ - \Lambda $ are measured near threshold with unprecedented precision. Preliminary results on the first measurement of the ^c form factor ratio |GE|/|GM| are also given. Ongoing analysis based on the high luminosity energy scan from 2015 and from radiative return at different $ \sqrt s $ are also described.