Proton Electromagnetic Form Factors Research Articles

The proton charge radius from dimuon photoproduction off the proton

We investigate the feasibility of measuring the proton charge radius through dimuon photoproduction off a proton target. Our findings indicate that the Bethe-Heitler mechanism, which dominates at small momentum transfers, allows for an extraction of the proton electromagnetic form factors in the extremely low Q2 region below 10−3 GeV2 in the spacelike region, when the incident photon beam energy exceeds several hundred MeV. The optimal kinematical region and a sensitivity study of the proton charge radius from dimuon photoproduction are presented. Such a measurement is expected to provide an alternative to the elastic muon-proton scattering measurements such as MUSE at PSI and AMBER at CERN.

Measurement of polarization transfer in the quasi-elastic [formula omitted] process

Polarization transfer to a bound proton in polarized electron knock-out reactions, A(e→,e′p→), is a powerful tool to look for an in-medium modification of the bound proton. It requires comparison to calculations that consider the many-body effects accompanying the quasi-free process. We report here measured components Px′, Pz′, and their ratio Px′/Pz′, of polarization transfer to protons bound in Ca40, which is described well by the shell model and for which reliable calculations are available. While the calculations capture the essence of the data, our statistical precision allows us to observe deviations that cannot be explained by simple scaling, including by varying the proton electromagnetic form factor ratio GE/GM. We further explore the deviations of the ratio of the polarization transfer components from that of a free proton, (Px′/Pz′)A/(Px′/Pz′)H, and its dependence on the bound-proton virtuality.

Impact of NNLO QED corrections on lepton-proton scattering at MUSE

We present the complete next-to-next-to-leading order (NNLO) pure pointlike QED corrections to lepton-proton scattering, including three-photon-exchange contributions, and investigate their impact in the case of the MUSE experiment. These corrections are computed with no approximation regarding the energy of the emitted photons and taking into account lepton-mass effects. We contrast the NNLO QED corrections to known next-to-leading order corrections, where we include the elastic two-photon exchange (TPE) through a simple hadronic model calculation with a dipole ansatz for the proton electromagnetic form factors. We show that, in the low-momentum-transfer region accessed by the MUSE experiment, the improvement due to more sophisticated treatments of the TPE, including inelastic TPE, is of similar if not smaller size than some of the NNLO QED corrections. Hence, the latter have to be included in a precision determination of the low-energy proton structure from scattering data, in particular for electron-proton scattering. For muon-proton scattering, the NNLO QED corrections are considerably smaller.

Chiral perturbation theory of the hyperfine splitting in (muonic) hydrogen

The ongoing experimental efforts to measure the hyperfine transition in muonic hydrogen prompt an accurate evaluation of the proton-structure effects. At the leading order in alpha , which is O(alpha ^5) in the hyperfine splitting (hfs), these effects are usually evaluated in a data-driven fashion, using the empirical information on the proton electromagnetic form factors and spin structure functions. Here we perform a first calculation based on the baryon chiral perturbation theory (Bchi PT). At leading orders it provides a prediction for the proton polarizability effects in hydrogen (H) and muonic hydrogen (mu H). We find large cancellations among the various contributions leading to, within the uncertainties, a zero polarizability effect at leading order in the Bchi PT expansion. This result is in significant disagreement with the current data-driven evaluations. The small polarizability effect implies a smaller Zemach radius R_textrm{Z}, if one uses the well-known experimental 1S hfs in H or the 2S hfs in mu H. We, respectively, obtain R_textrm{Z}(textrm{H}) = 1.010(9) fm, R_textrm{Z}(mu textrm{H}) = 1.040(33) fm. The total proton-structure effect to the hfs at O(alpha ^5) is then consistent with previous evaluations; the discrepancy in the polarizability is compensated by the smaller Zemach radius. Our recommended value for the 1S hfs in mu text {H} is 182.640(18),textrm{meV}.

Nucleon Electromagnetic Form Factors Measurements at BESIII

Electromagnetic form factors provide fundamental information to reveal the internal structure and dynamincs of nucleons. Using the energy scan data collected by BESIII experiment on BEPCII collider, the Born cross section of e+e−→pp¯ and e+e−→nn¯, and the proton and neutron electromagnetic form factors are measured at center-of-mass energies between 2.0 and 3.08 GeV, through the e+e− direct annihilation process. Through the initial-state-radiation process, the proton electromagnetic form factors are also measured from the pp¯ threshold to 3.0 GeV with the large data sets collected at center-of-mass energy between 3.773 and 4.6 GeV, while the Born cross section of e+e−→pp¯ is measured up to 3.8 GeV.

Interpretation of recent form factor data in terms of an advanced representation of baryons in space and time

Data on electromagnetic form factors of proton, neutron, and $\mathrm{\ensuremath{\Lambda}}$ from annihilation and scattering reactions are collected and interpreted in the frame of a generalized picture of the internal structure of baryons which holds in space-like and time-like regions. It is shown that these data give an insight into the spatial structure of the baryon for distances 100 times smaller than the baryon size and, in the time-like region, a vision of the time evolution of the hadronic matter for times up to ${10}^{\ensuremath{-}25}$ s, that is two orders of magnitude shorter than the time taken by the light to cross the volume of a proton. In the proposed interpretation, the electric form factor of the proton in the space-like region cannot cross zero, but vanishes or stays very small, as an extrapolation of the data seems to show. In the time-like region specific structures appearing in the data give evidence of the dominance of the quark-diquark underlying dynamics in a well-determined time interval during the evolution of the system.

Magnetic moments of the octet, decuplet, low-lying charm, and low-lying bottom baryons in a nuclear medium

Abstract We study the magnetic moments of the octet, decuplet, low-lying charm, and low-lying bottom baryons with nonzero light quarks in symmetric nuclear matter using the quark–meson coupling (QMC) model, which satisfies the constraint for the allowed maximum change (swelling) of the in-medium nucleon size derived from the y-scaling data for 3He(e, e′) and 56Fe(e, e′). This is the first study to estimate the in-medium magnetic moments of the low-lying charm and bottom baryons with nonzero light quarks. The present QMC model also satisfies the expected allowed maximum enhancement of the nucleon magnetic moments in nuclear matter. Moreover, it has been proven that the calculated in-medium to free proton electromagnetic form factor (EMFF) ratios calculated within the QMC model reproduce well the proton EMFF super ratio extracted from $^4{\rm He}(\vec{e},e^{\prime }\vec{p})^3{\rm H}$ at Jefferson Laboratory. The medium modifications of the magnetic moments are estimated by evaluating the in-medium to free space baryon magnetic moment ratios to compensate the MIT bag deficiency to describe the free space octet baryon magnetic moments, where ratios are often measured directly in experiments even without knowing the absolute values, such as the free and bound proton electromagnetic form factors, as well as the European Muon Collaboration effect to extract the structure function F2 ratio of the bound to free nucleons by the corresponding cross section ratio. We also present the results calculated with the different current quark mass values for the strange and bottom quarks to see the possible impact. Furthermore, for practical use we give the explicit density-dependent parametrizations for the vector potentials of the baryons and light-(u, d) quarks, as well as for the effective masses of the baryons treated in this study, and of the mesons ω, ρ, K, K*, η, $\eta^{\prime}$, D, D*, B, and B*.

Proton Electromagnetic Form Factors in the Time-like Region through the Scan Technique

For over 100 y, scientists have investigated the properties of the proton, which is one of the most abundant components of visible matter in the universe. Nevertheless, researchers do not fully understand many details about its internal structure and dynamics. Time-like electromagnetic form factors are some of the observable quantities that can help us achieve a deeper understanding. In this review article, we present an overview of the current experimental status in this field, consisting of measurements of the time-like reactions e+e−→pp¯ and pp¯→e+e− and future measurements of pp¯→μ+μ−. The focus is put on recent high-precision results of the reaction e+e−→pp¯ that have been obtained after analyzing 688.5 pb−1 of data taken at the BESIII experiment. They are compared to and put into perspective with results from previous measurements in this channel. We discuss the channels pp¯→e+e− and pp¯→μ+μ− in terms of the few existing, as well as future measurements, which the PANDA experiment will perform. Finally, we review several new theoretical models and phenomenological approaches inspired by the BESIII high-precision results and then discuss their implications for a deeper understanding of the proton’s structure and inner dynamics.

Time-like Proton Form Factors with Initial State Radiation Technique

Electromagnetic form factors are fundamental quantities describing the internal structure of hadrons. They can be measured with scattering processes in the space-like region and annihilation processes in the time-like region. The two regions are connected by crossing symmetry. The measurements of the proton electromagnetic form factors in the time-like region using the initial state radiation technique are reviewed. Recent experimental studies have shown that initial state radiation processes at high luminosity electron-positron colliders can be effectively used to probe the electromagnetic structure of hadrons. The BABAR experiment at the B-factory PEP-II in Stanford and the BESIII experiment at BEPCII (an electron positron collider in the τ-charm mass region) in Beijing have measured the time-like form factors of the proton using the initial state radiation process e+e−→pp¯γ. The two kinematical regions where the photon is emitted from the initial state at small and large polar angles have been investigated. In the first case, the photon is in the region not covered by the detector acceptance and is not detected. The Born cross section and the proton effective form factor have been measured over a wide and continuous range of the the momentum transfer squared q2 from the threshold up to 42 (GeV/c)2. The ratio of electric and magnetic form factors of the proton has been also determined. In this report, the theoretical aspect and the experimental studies of the initial state radiation process e+e−→pp¯γ are described. The measurements of the Born cross section and the proton form factors obtained in these analyses near the threshold region and in the relatively large q2 region are examined. The experimental results are compared to the predictions from theory and models. Their impact on our understanding of the nucleon structure is discussed.

Elucidating the ρ-meson’s role as intermediate resonance in the time-like electromagnetic pion form factor

Motivated by the planned measurements of the time-like electromagnetic proton form factors an exploratory study of the time-like electromagnetic pion form factor is presented in a formalism which describes mesons as Poincaré-invariant bound states. In the respective quark interaction kernel, beyond the gluon-intermediated interactions for valence-type quarks, non-valence effects are included by allowing the pions to couple back in a self-consistent manner to the quarks. Consequently, the opening of the dominant ρ decay channel, ρ → ππ, and the presence of a multi-particle branch cut, setting in when the two-pion threshold is crossed, are included consistently, first in the correspondingly calculated quark-photon vertex, and then consequently in the time-like electromagnetic pion form factor. The obtained results are in agreement with the available experimental data and provide further evidence for the effcacy of a vector-meson dominance model. Effects of going beyond the here employed isospin-symmetric limit are discussed. Last but not least, an outlook is provided on how to include in Poincaré-covariant Faddeev approaches the effects of intermediate resonances in the calculation of baryon properties.

Prediction of neutron electromagnetic form factors behaviors just by the proton electromagnetic form factors data

First time a theoretical prediction of the neutron electromagnetic form factors behaviors in the whole region of their definition by the use of the proton electromagnetic form factors data only is demonstrated. This could be achieved in the framework of the unitary and analytic approach to a description of the nucleon electromagnetic form factors with canonical normalization conditions, the QCD (up to the logarithmic correction) asymptotic behaviors and specific transformation properties of the nucleon electromagnetic current in the isotopic space.

Semiexclusive dilepton production in proton-proton collisions with one forward proton measurement at the LHC

We discuss photon-photon fusion mechanisms of dilepton production in proton-proton collisions with rapidity gap in the main detector and one forward proton in the forward proton detectors. This is relevant for the LHC measurements by ATLAS+AFP and CMS+PPS. Transverse momenta of the intermediate photons are taken into account and photon fluxes are expressed in terms of proton electromagnetic form factors and structure functions. Differential distributions in $\xi_{1/2}$, $M_{ll}$, $Y_{ll}$, $p_{t,ll}$, $M_R$ %pamietac wyjasnic M_R w tekscie are shown and the competition of different mechanisms is discussed. Both double-elastic and single-dissociative processes are included in the analysis. Different parametrizations of the structure functions are used. We discuss also mechanism with one forward $\Delta^+$ isobar, or other proton resonances in the final state. The role of several cuts is studied. We also use SuperChic generator and compare corresponding results to the results of our codes. The soft rapidity gap survival factor is calculated for each contribution separately. The gap survival factor for the single-dissociative mechanism due to minijet emission into the main detector is calculated in addition. It depends on the type of contribution (fully elastic, single dissociation, double dissociation). The soft rapidity gap survival factor for the case of single proton measurement is significantly smaller than that for the inclusive case (no proton measurement). We find only weak dependence on the invariant mass of the dilepton system as well as the lepton pair transverse momentum and sizeable dependence on the pair rapidity. The latter effect is rather difficult to identify experimentally.

Polarization transfer in $$\varvec{e}^+p \rightarrow e^+ \varvec{p}$$ scattering using the Super BigBite Spectrometer

The effects of multi-photon-exchange and other higher-order QED corrections on elastic electron-proton scattering have been a subject of high experimental and theoretical interest since the polarization transfer measurements of the proton electromagnetic form factor ratio \(G_E^p/G_M^p\) at large momentum transfer \(Q^2\) conclusively established the strong decrease of this ratio with \(Q^2\) for \(Q^2 \gtrsim 1\) \(\hbox {GeV}^2\). This result is incompatible with previous extractions of this quantity from cross section measurements using the Rosenbluth Separation technique. Much experimental attention has been focused on extracting the two-photon exchange (TPE) effect through the unpolarized \(e^+p/e^-p\) cross section ratio, but polarization transfer in polarized elastic scattering can also reveal evidence of hard two-photon exchange. Furthermore, it has a different sensitivity to the generalized TPE form factors, meaning that measurements provide new information that cannot be gleaned from unpolarized scattering alone. Both \(\epsilon \)-dependence of polarization transfer at fixed \(Q^2\), and deviations between electron-proton and positron-proton scattering are key signatures of hard TPE. A polarized positron beam at Jefferson Lab would present a unique opportunity to make the first measurement of positron polarization transfer, and comparison with electron-scattering data would place valuable constraints on hard TPE. Here, we propose a measurement program in Hall A that combines the Super BigBite Spectrometer for measuring recoil proton polarization, with a non-magnetic calorimetric detector for triggering on elastically scattered positrons. Though the reduced beam current of the positron beam will restrict the kinematic reach, this measurement will have very small systematic uncertainties, making it a clean probe of TPE.

Measurement of proton electromagnetic form factors in the time-like region using initial state radiation at BESIII

The electromagnetic process e+e−→pp¯ is studied with the initial-state-radiation technique using 7.5 fb−1 of data collected by the BESIII experiment at seven energy points from 3.773 to 4.600 GeV. The Born cross section and the effective form factor of the proton are measured from the production threshold to 3.0 GeV/c2 using the pp¯ invariant-mass spectrum. The ratio of electric and magnetic form factors of the proton is determined from the analysis of the proton-helicity angular distribution.

Measurement of the Charge-Averaged Elastic Lepton-Proton Scattering Cross Section by the OLYMPUS Experiment.

We report the first measurement of the average of the electron-proton and positron-proton elastic scattering cross sections. This lepton charge-averaged cross section is insensitive to the leading effects of hard two-photon exchange, giving more robust access to the proton's electromagnetic form factors. The cross section was extracted from data taken by the OLYMPUS experiment at DESY, in which alternating stored electron and positron beams were scattered from a windowless gaseous hydrogen target. Elastic scattering events were identified from the coincident detection of the scattered lepton and recoil proton in a large-acceptance toroidal spectrometer. The luminosity was determined from the rates of Møller, Bhabha, and elastic scattering in forward electromagnetic calorimeters. The data provide some selectivity between existing form factor global fits and will provide valuable constraints to future fits.

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.

Feasibility studies for the measurement of time-like proton electromagnetic form factors from bar{p}p rightarrow mu ^+mu ^- at overline{text {P}}text {ANDA} at FAIR

This paper reports on Monte Carlo simulation results for future measurements of the moduli of time-like proton electromagnetic form factors, |G_{E}| and |G_{M}|, using the bar{p} p rightarrow mu ^{+} mu ^{-} reaction at overline{text {P}}text {ANDA} (FAIR). The electromagnetic form factors are fundamental quantities parameterizing the electric and magnetic structure of hadrons. This work estimates the statistical and total accuracy with which the form factors can be measured at overline{text {P}}text {ANDA}, using an analysis of simulated data within the PandaRoot software framework. The most crucial background channel is bar{p} p rightarrow pi ^{+} pi ^{-}, due to the very similar behavior of muons and pions in the detector. The suppression factors are evaluated for this and all other relevant background channels at different values of antiproton beam momentum. The signal/background separation is based on a multivariate analysis, using the Boosted Decision Trees method. An expected background subtraction is included in this study, based on realistic angular distributions of the background contribution. Systematic uncertainties are considered and the relative total uncertainties of the form factor measurements are presented.

Energy interval 3S−1S in muonic hydrogen

The energy interval $ (3S-1S) $ in muonic hydrogen is calculated on the basis of quasipotential approach in quantum electrodynamics. We take into account different corrections of orders $\alpha^3\div \alpha^6 $, which are determined by relativistic effects, the effects of vacuum polarization, nuclear structure and recoil, as well as combined corrections including the above. Nuclear structure effects are expressed in terms of the charge radius of the proton in the case of one-photon interaction and the proton electromagnetic form factors in the case of two-photon exchange interaction. The value of the energy interval (3S-1S) can be used for a comparison with future experimental data and determining the proton charge radius with greater accuracy.

Determination of the proton charge radius from the study of the hydrogen S-energy levels

On the basis of quasipotential method in quantum electrodynamics, the energy interval (3S – 1S) in muonic hydrogen is calculated. The corrections of orders α 3, α 4, α 5, α 6 are taken into account, which are determined by relativistic effects, the effects of vacuum polarization, nuclear structure and recoil, as well as combined corrections. In the leading order proton structure effects are expressed in terms of the charge radius of the proton. In the case of two-photon exchange interaction proton structure corrections are determined by the proton electromagnetic form factors. The value of the energy interval (3S – 1S) can be used for comparison with future experimental data and determining the proton charge radius with greater accuracy.

How analytic choices can affect the extraction of electromagnetic form factors from elastic electron scattering cross section data

Scientists often try to incorporate prior knowledge into their regression algorithms, such as a particular analytic behavior or a known value at a kinematic endpoint. Unfortunately, there is often no unique way to make use of this prior knowledge, and thus, different analytic choices can lead to very different regression results from the same set of data. To illustrate this point in the context of the proton electromagnetic form factors, we use the Mainz elastic data with its 1422 cross section points and 31 normalization parameters. Starting with a complex unbound non-linear regression, we will show how the addition of a single theory-motivated constraint removes an oscillation from the magnetic form factor and shifts the extracted proton charge radius. We then repeat both regressions using the same algorithm, but with a rebinned version of the Mainz dataset. These examples illustrate how analytic choices, such as the function that is being used or even the binning of the data, can dramatically affect the results of a complex regression. These results also demonstrate why it is critical when using regression algorithms to have either a physical model in mind or a firm mathematical basis