Proton Form Factors Research Articles

Novel approach to the global analysis of proton form factors in elastic electron-proton scattering

We present a method for the global analysis of elastic electron-proton scattering when combining data sets from experiments with different overall normalization uncertainties. The method is a modification of one employed by the NNPDF collaboration in the fitting of parton distribution data. This method is an alternative to the ‘penalty trick’ method traditionally employed in global fits to proton electric and magnetic form factors, while avoiding the statistical biases inherent in that approach. We discuss issues that arise when extending the method to nonlinear models. For data with Q2>1GeV2 we find relatively minor differences to traditional model fits when the normalization uncertainties from different experiments are correctly accounted for. We discuss implications of this method for the well-known discrepancy between the form factor ratio GE/GM extracted from the Rosenbluth and polarization transfer techniques. Published by the American Physical Society 2024

Recent results of baryon EM form factors at BESIII

Precise experimental measurements of the baryon form factors are a test-bed for understanding the baryon’s properties and dynamical behavior emerge from QCD. With high statistics, the cross section of e+e− → pp and e+e− → nn are both measured with the highest precision in a wide q2 range. The oscillation behavior on the proton and neutron effective form factor is updated with SND result. With the ISR technique, the form factor measurement can reach as low as the mass threshold of pp or nn. Analyticity of nucleon form factors is discussed. Moreover, new results about the hyperon (Λ, Λc, Σ, Ω, ∆) form factors are presented in this talk. Some similar behaviors appear on the hyperon form factors which will help to understand the internal structure or interactions inside of the baryon. The complete determination of EMFFs of Λ and Σ has been carried on and provides a new insight of EMFFs in time-like region.

At the heart of the proton

Two main findings on electromagnetic hadron form factors focussed a large interest of the hadron physics community in the recent years. One is the decrease of the electric to magnetic form factor ratio when the momentum transfer in electron proton elastic scattering increases. The second is the discovery of regular oscillations of the generalized proton form factors in the annihilation process electron-positron into proton-antiproton. In this talk we propose a coherent interpretation of these findings giving a general, dynamical description of the proton in the space-time frame which is based on the presence of a quantum vacuum at very small distances.

Note on the electromagnetic radius of proton

In this paper, we have analyzed the proton form factor data by using a number of phenomenological parametrizations (models) and extracting the proton electric and magnetic radii. To this end, we performed a global fit to all available form factor data, with the virtual photon momentum squared [Formula: see text] from [Formula: see text] to nearly 10[Formula: see text]GeV2 for electric form factor and from [Formula: see text] to 31[Formula: see text]GeV2 for magnetic one. Special attention was given to the small structure shown by the form factor data near [Formula: see text][Formula: see text]GeV2. It was found that different models yield different structures with different numbers of minimum at this kinematics. Since the slope of form factor in the limit of [Formula: see text] is influenced by this structure, the extracted proton radii are consequently different for different models. Our finding recommends that future experiments should focus on this kinematics instead of low [Formula: see text]. Experimental data with accuracies comparable to those of the latest data at low [Formula: see text] would clearly help to clarify the effect of this structure on the proton charge radius. Interestingly, most of the extracted proton charge radii were found to be closer to the value obtained from the muonic hydrogen atom spectroscopy.

Study of damped oscillating structures from charged and neutral K-meson electromagnetic form factors data

The damped oscillating structures were recently revealed in the proton “effective” form factor data. For the time being they can neither be confirmed nor disproved by investigations of the individual proton form factors data because the data have not yet achieved the required level of precision. On the other hand, conjectures that the oscillating structures are direct manifestations of the quark-gluon structure of the proton indicate that they should not be specific only to the proton and neutron. This opens a possibility to find these structures also in the data of other hadrons by the same procedure as for the proton. In this paper the oscillatory structures are investigated in the electromagnetic form factor data of the charged and neutral K-mesons. If the charged and neutral K-meson data are described by the three parametric formula by means of which the oscillating structures have been revealed for the proton (although with a large value of chi ^2/ndf) then oscillating structures appear. On the other hand, if the physically well founded Unitary and Analytic model of the K-meson electromagnetic structure is used for the description of the charged K-meson data, no damped oscillating structures are visible. However, in the case of the neutral K-meson data one cannot make a definite conclusion, and more precise data are needed. These results indicate that also the damped oscillating structures obtained from the “effective” proton form factor data are likely an artefact of the three parametric formula, which cannot describe the data with sufficient precision.

Gluon gravitational form factors of protons from charmonium photoproduction* *Supported by the National Natural Science Foundation of China (12065014, 12047501), the Natural Science Foundation of Gansu province, China (22JR5RA266). We acknowledge the West Light Foundation of the Chinese Academy of Sciences (21JR7RA201)

Inspired by the recent near-threshold photoproduction measurements, we discuss gluon gravitational form factors (GFFs) and internal properties of the proton. This work presents a complete analysis of the proton gluon GFFs connecting the gluon part of the energy-momentum tensor and the heavy quarkonium photoproduction. In particular, a global fitting of the differential and total cross section experimental data is used to determine the gluon GFFs as functions of the squared momentum transfer t. Combined with the quark contributions to the D-term form factor extracted from the deeply virtual Compton scattering experiment, the total D-term is obtained to investigate their applications in describing the proton mechanical properties. These studies provide a unique perspective on investigating the proton gluon GFFs and important information for enhancing QCD constraints on the gluon GFFs.

Search for Damped Oscillating Structures from Charged Pion Electromagnetic Form Factor Data

The damped oscillating structures recently revealed by a three parametric formula from the proton “effective” form factor data extracted of the measured total cross section σtotbare(e+e−→pp¯) still seem to have an unknown origin. The conjectures of their direct manifestation of the quark-gluon structure of the proton indicate that they are not specific only of the proton and neutron, but they have to be one’s own, similar to other hadrons. Therefore, the oscillatory structures from the charged pion electromagnetic form factor timelike data, extracted of the process e+e−→π+π− are investigated by using the same procedure as in the case of the proton. The analysis shows the appearance of the oscillating structures in the description of the charged pion electromagnetic form factor timelike data by three parametric formula with a rather large value of χ2/ndf, while the description of the data by the physically well-founded Unitary and Analytic model has not revealed any damped oscillating structures. From the obtained result on the most simple object of strong interactions, one can conclude that damped oscillating structures received from the “effective” proton form factor data are probably generated by a utilization of the improper three parametric formula which does not describe these data with sufficient precision.

J/ψ Near-Threshold Photoproduction off the Proton and Neutron with CLAS12

Near-threshold J/ψ photoproduction is a key aspect of the physics program at the Thomas Jefferson National Accelerator Facility (JLab) 12 GeV upgrade due to the wealth of information it has to offer. J/ψ photoproduction proceeds through the exchange of gluons in the t-channel and is expected to provide unique insight about the nucleon gravitational form factors and the nucleon mass radius. The JLab based CLAS Collaboration, which uses the CEBAF Large Acceptance Spectrometer (CLAS12), aims to measure the J/ψ near threshold photoproduction cross section using both a proton and a deuteron target, from threshold up to 10.6 GeV. The deuteron target further offers the possibility of comparing the proton and neutron gluonic form factors and mass radii in a first measurement of the cross sections off a proton or neutron within the deuteron target. The analysis towards these measurements is ongoing and well advanced, with machine learning based techniques for particle identification already designed and validated with CLAS12 data.

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.

Experimental study of the e^+e^-rightarrow n{bar{n}} process at the VEPP-2000 e^+e^- collider with the SND detector

The process e^+e^-rightarrow n{bar{n}} is studied in the experiment at the VEPP-2000 e^+e^- collider with the SND detector. The technique of the time measurements in the multichannel NaI(Tl) electromagnetic calorimeter is used to select n{bar{n}} events. The value of the measured cross section in the center-of-mass energy range from 1.894 to 2 GeV varies from 0.5 to 0.35 nb. The effective neutron timelike form factor is derived from the measured cross section and compared with the proton form factor. The ratio of the neutron electric and magnetic form factors is obtained from the analysis of the antineutron polar angle distribution and found to be consistent with unity.

Proton gravitational form factors in a light-front quark-diquark model

We present a recent calculation of the gravitational form factors (GFFs) of proton using the light-front quark-diquark model constructed by the soft-wall AdS/QCD[1]. The four GFFs ~A(Q^2)A(Q2) , B(Q^2)B(Q2) , C(Q^2)C(Q2) and \bar{C}(Q^2)C‾(Q2) are calculated in this model. We also show the pressure and shear distributions of quarks inside the proton. The GFFs, A(Q^2)A(Q2) and B(Q^2)B(Q2) are found to be consistent with the lattice QCD, while the qualitative behavior of the DD-term form factor is in agreement with the extracted data from the deeply virtual Compton scattering (DVCS) experiments at JLab, the lattice QCD, and the predictions of different phenomenological models.

Proton gravitational form factors and mechanical properties in a light-front quark-diquark model

We present our recent calculation of the gravitational form factors (GFFs) of proton using the light-front quark-diquark model constructed by the soft-wall AdS/QCD. We extract the four quark GFFs by calculating the matrix elements of the symmetric energy momentum tensor. Using the D-term we calculate the pressure and shear distributions of quarks inside the proton in the impact parameter space. The GFFs, A(Q2) and B(Q2) are found to be consistent with the lattice QCD, while the qualitative behavior of the D-term form factor is in agreement with the extracted data from the deeply virtual Compton scattering (DVCS) experiments at JLab, the lattice QCD, and the predictions of different phenomenological models.

Matter Density Distributions and Reaction Cross Sections for 8Li and 22N Exotic Nuclei

The Harmonic Oscillator (HO) and Gaussian (GS) wave functions within the Binary Cluster Model (BCM) were employed to investigate neutron, proton and matter densities of the ground state as well as the elastic proton form factors of one neutron 8Li and 22N halo nuclei. The long tail is a property that is clearly shown in the neutron density. The existence of a long tail in the neutron densities of 8Li and 22N indicates that these nuclei have a neutron halo structure. Moreover, the matter rms radii and the reaction cross section of these nuclei were calculated using the Glauber model.

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.

Proton and neutron form factors from deformed gravity/gauge duality

In this work we study the electric and magnetic Sachs form factors for proton and neutron by using a deformed gravity/gauge model. We describe holographically baryons as well as gauge bosons which are ruled by the parameters kB and kγ, associated with confinement and kinematical energy scales, respectively. Then, we construct the interaction action and calculate the electric and magnetic form factors for the proton and the neutron, and their electromagnetic sizes. The obtained results are compatible with those found in the literature from experimental and theoretical data.

Color transparency and the proton form factor: Evidence for the Feynman mechanism

A recent experiment [{\bf Phys. Rev. Lett. 126,082301 (2021)}] used the $(e,e'p)$ reaction on $^{12}$C to search for the effects of color transparency (the absence of final state interactions). Color transparency was said to be ruled out. The ability to observe the effects of color transparency depends on the ability of a putative point-like-configuration (PLC), formed in a high-momentum transfer coherent reaction, to escape the nucleus without expanding its size. We study the expansion aspect of color transparency using superconformal baryon-meson symmetry and light-front holographic QCD. A new formalism is obtained and used to analyze the recent experiment. The resulting conclusion is that effects of expansion would not be sufficiently significant in causing final state interactions to occur. Therefore we conclude that a PLC was not formed. This means that the Feynman mechanism involving virtual photon absorption on a single high momentum quark is responsible for high momentum electromagnetic form factor of the proton.

Proton and neutron form factors with quark orbital excitations

Nucleon form factors play an especially important role in studying the dynamics of nucleons and explicit structure of the wave functions at arbitrary nucleon velocity. The purpose of the paper is to explain theoretically all four nucleon form factors measured experimentally in the cross section measurements (by the Rosenbluth method), yielding almost equal normalized form factors $G^p_E,G^p_M,G^n_M$, as well as in the polarization transfer experiments, where a strongly decreasing proton electric form factor has been discovered. It is shown, using relativistic hyperspherical formalism, that the nucleon wave functions in the lowest approximation provide almost equal normalized form factors as seen in the Rosenbluth cross sections, but in the higher components they contain a large admixture of the quark orbital momenta, which strongly decreases $G^p_E$ and this effect is possibly detected in the polarization transfer method (not seen in the classical cross section experiments). Moreover, the same admixture of the higher components explains the small positive form factor $G^n_E$. The resulting form factors, $G^p_M(Q),G^p_E(Q),G^n_M(Q)$ are calculated up to $Q^2\approx 10$ GeV$^2$, using the standard and the Lorentz contracted wave functions and shown to be in reasonable agreement with experimental data.

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.