Electric Form Factor Research Articles

Hadronic structure on the light front. VIII. Light scalar and vector mesons

We use the QCD instanton vacuum model to discuss the emergence of the light scalar and vector mesons on the light front. We take into account both the instanton and anti-instanton single and molecular interactions on the light quarks, in the form of nonlocal effective interactions. Although the molecular induced interactions are suppressed by a power of the packing fraction, they are still sufficient to bind the vector mesons, while keeping most of the scalar spectrum relatively unchanged. We explicitly derive the light front distribution amplitudes and partonic functions for the scalar and vector mesons, and compare them after pertinent QCD evolution, to the available empirical and lattice measured counterparts. The Dirac electric form factors for both the pion and ρ meson are derived, and shown to compare well with current data. Published by the American Physical Society 2024

Determination of the Σ^{+} Timelike Electromagnetic Form Factors.

Based on data samples collected with the BESIII detector at the BEPCII collider, the process e^{+}e^{-}→Σ^{+}Σ[over ¯]^{-} is studied at center-of-mass energies sqrt[s]=2.3960, 2.6454, and 2.9000GeV. Using a fully differential angular description of the final state particles, both the relative magnitude and phase information of the Σ^{+} electromagnetic form factors in the timelike region are extracted. The relative phase between the electric and magnetic form factors is determined to be sinΔΦ=-0.67±0.29(stat)±0.18(syst) at sqrt[s]=2.3960 GeV, ΔΦ=55°±19°(stat)±14°(syst) at sqrt[s]=2.6454 GeV, and 78°±22°(stat)±9°(syst) at sqrt[s]=2.9000 GeV. For the first time, the phase of the hyperon electromagnetic form factors is explored in a wide range of four-momentum transfer. The evolution of the phase along with four-momentum transfer is an important input for understanding its asymptotic behavior and the dynamics of baryons.

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

Elastic neutrino scattering on nucleons and neutrino electromagnetic properties

We study the electromagnetic contribution to elastic neutrino-nucleon scattering processes. The neutrino electromagnetic charge, magnetic, electric, and anapole form factors of both diagonal and transition types in the mass basis are taken into account in the present formalism. When treating the nucleon electromagnetic vertex, we take into account not only the charge and magnetic form factors of a nucleon, but also its electric and anapole form factors. We examine the effects of the neutrino magnetic moment on elastic neutrino-nucleon scattering and how they can be disentangled from those of the strange form factors contributions to the nucleon’s weak neutral current.

Electromagnetic form factors at low energy elastic electron–proton scattering

The prediction of quantum electrodynamics for elastic electron–proton scattering needs further modifications to agree with experimental data. Two scattering mechanisms that may occur are the forward and backward scattering angles for four-momentum transfer [Formula: see text] up to 0.8 (GeV/[Formula: see text])2. This is due to two different scattering centers. But the forward scattering is observed only at relatively high values of [Formula: see text][Formula: see text](GeV/[Formula: see text])2. The modifications related to the electric and magnetic form factors characterize the proton’s internal structure. These form factors’ dependence on [Formula: see text] provides good agreement with other analysis methods. The proton’s charge radius, which corresponds to the maximum value of the scattering radius, is [Formula: see text][Formula: see text]fm. The scattered electron is sensitive to proton internal constituents, especially at high values of [Formula: see text] in which both scattering radius and photon wavelength decrease.

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.

Laser-assisted electron–nucleon scattering

In the absence and presence of a circularly polarized monochromatic electromagnetic pulse, we have analyzed the electron–nucleon scattering process, where the nucleon is assumed to be spinless with a spherical shape. We have provided the theoretical calculation of the differential cross section (DCS) by using the Dirac–Volkov formalism. This research paper aims to provide two comparisons: We first compare the DCS in the absence of the laser field with its corresponding laser-assisted DCS. A second comparison is made between the electron–proton and electron–neutron scattering processes to study the effect of the laser on both processes. The results obtained about the effect of the laser field on the DCS and the electric form factor have been discussed for both scattering processes. We have found that the DCS is reduced when the laser field is applied for both processes. In addition, the form factor is also decreased by raising the incident electron energy in electron–proton scattering, but it increases in electron–neutron scattering. Moreover, the form factors for both scattering situations are unchanged by raising the laser field strength up to [Formula: see text].

Measurements of the Electric and Magnetic Form Factors of the Neutron for Timelike Momentum Transfer.

We present the first measurements of the electric and magnetic form factors of the neutron in the timelike (positive q^{2}) region as function of four-momentum transfer. We explored the differential cross sections of the reaction e^{+}e^{-}→n[over ¯]n with data collected with the BESIII detector at the BEPCII accelerator, corresponding to an integrated luminosity of 354.6 pb^{-1} in total at twelve center-of-mass energies between sqrt[s]=2.0-2.95 GeV. A relative uncertainty of 18% and 12% for the electric and magnetic form factors, respectively, is achieved at sqrt[s]=2.3935 GeV. Our results are comparable in accuracy to those from electron scattering in the comparable spacelike region of four-momentum transfer. The electromagnetic form factor ratio R_{em}≡|G_{E}|/|G_{M}| is within the uncertainties close to unity. We compare our result on |G_{E}| and |G_{M}| to recent model predictions, and the measurements in the spacelike region to test the analyticity of electromagnetic form factors.

Hamiltonian sensitivity in calculating the electromagnetic moments and electroexcitation form factor for the sd nuclei using shell model with Skyrme–Hartree–Fock

In this work, the nuclear electromagnetic moments for the ground and low-lying excited states for sd shell nuclei have been calculated, resulting in a revised database with 56 magnetic dipole moments and 41 electric quadrupole moments. The shell model calculations are performed for each sd isotope chain, considering the sensitivity of changing the sd two-body effective interactions USDA, USDE, CWH and HBMUSD in the calculation of the one-body transition density matrix elements. The calculations incorporate the single-particle wave functions of the Skyrme interaction to generate a one-body potential in Hartree–Fock theory to calculate the single-particle matrix elements. For most sd shell nuclei, the experimental data are well reproduced, except for those spans near the island of inversion. In order to interpret the structure of low-lying excited states, the electric quadrupole and magnetic dipole transition form factors and the corresponding reduced transition probabilities in the sd shell nuclei have also been calculated, for which the experimental data are available. The present results demonstrate the nuclear electromagnetic moments’ sensitivity to many forms of the understanding of nucleon–nucleon interactions and provide a crucial baseline for future improvements in conceptual calculations.

The electromagnetic Sigma-to-Lambda transition form factors with coupled-channel effects in the space-like region

Using dispersion theory, the electromagnetic Sigma-to-Lambda transition form factors are expressed as the product of the pion electromagnetic form factor and the Sigma {bar{varLambda }}rightarrow pi pi scattering amplitudes with the latter estimated from SU(3) chiral perturbation theory including the baryon decuplet as explicit degrees of freedom. The contribution of the K{bar{K}} channel is also taken into account and the pi pi –K{bar{K}} coupled-channel effect is included by means of a two-channel Muskhelishvili–Omnès representation. It is found that the electric transition form factor shows a significant shift after the inclusion of the K{bar{K}} channel, while the magnetic transition form factor is only weakly affected. However, the K{bar{K}} effect on the electric form factor is obscured by the undetermined coupling h_A in the three-flavor chiral Lagrangian. The error bands of the Sigma-to-Lambda transition form factors from the uncertainties of the couplings and low-energy constant in three-flavor chiral perturbation theory are estimated by a bootstrap sampling method.

Properties of Pb208 predicted from the relativistic equation of state in the full Dirac space

Relativistic Brueckner-Hartree-Fock (RBHF) theory in the full Dirac space allows one to determine uniquely the momentum dependence of scalar and vector components of the single-particle potentials. In order to extend this new method from nuclear matter to finite nuclei, as a first step, properties of $^{208}\mathrm{Pb}$ are explored by using the microscopic equation of state for asymmetric nuclear matter and a liquid droplet model. The neutron and proton density distributions, the binding energies, the neutron and proton radii, and the neutron skin thickness in $^{208}\mathrm{Pb}$ are calculated. In order to further compare the charge densities predicted from the RBHF theory in the full Dirac space with the experimental charge densities, the differential cross sections and the electric charge form factors in the elastic electron-nucleus scattering are obtained by using the phase-shift analysis method. The results from the RBHF theory are in good agreement with the experimental data. In addition, the uncertainty arising from variations of the surface term parameter ${f}_{0}$ in the liquid droplet model is also discussed.

Understanding the systematic differences in extractions of the proton electric form factors at low Q2

Systematic differences exist between values of the proton's electric form factors in the low-$Q^2$ region extracted by different experimental and theoretical groups, though they are all making use of basically the same electron-proton scattering data. To try understand the source of these differences, we make use of the analytically well-behaved rational (N=1, M=1) function, a predictive function that can be reasonably used for extrapolations at $Q^{2} \rightarrow 0$. First, we test how well this deceptively simple two-parameter function describes the extremely complex and state-of-the-art dispersively improved chiral effective field theory calculations. Second, we carry out a complete re-analysis of the 34 sets of eletron-proton elastic scattering cross-section data of the Mainz A1 Collaboration with its unconstrained 31 normalization parameters up to $Q^{2} = 0.5~{\rm (GeV/c)^{2}}$. We find that subtle shifts in the normalization parameters can result in relatively large changes in the extracted physical qualities. In conclusion, we show that by simply using a well-behaved analytic function, the apparent discrepancy between recent form-factor extractions can be resolved.

The lowest excited states of 14C and 14O nuclei within a five-cluster model

We study the ground and the first excited 0+ states of two mirror nuclei 14C and 14O within a five cluster model (three alpha-particles and two extra nucleons) with the use of high accuracy variational approach with Gaussian bases. The first excited 0+ state of these nuclei is shown to be connected with a change of the structure of the two nucleon subsystem moving in the field of the 12C cluster. The density distributions, electric form factors (both the elastic and transition ones), pair correlation functions, and the momentum distributions of the constituent particles are found. The most probable shapes of five-cluster systems are revealed.

Low- Q2 elastic electron-proton scattering using a gas jet target

In this paper, we describe an experiment measuring low-$Q^2$ elastic electron-proton scattering using a newly developed cryogenic supersonic gas jet target in the A1 three-spectrometer facility at the Mainz Microtron. We measured the proton electric form factor within the four-momentum transfer range of $0.01\le Q^2 \le 0.045(\text{GeV/c})^2$. The experiment showed consistent results with the existing measurements. The data we collected demonstrated the feasibility of the gas jet target and the potential of future scattering experiments using high-resolution spectrometers with this gas jet target.

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.

Definition of Local Spatial Densities in Hadrons.

We show that the matrix element of a local operator between hadronic states can be used to unambiguously define the associated spatial density. As an explicit example, we consider the charge density of a spinless particle and clarify its relationship to the electric form factor. Our results lead to an unconventional interpretation of the spatial densities of local operators and their moments.

Precision nucleon charges and form factors using ( 2+1 )-flavor lattice QCD

We present a high statistics study of the isovector nucleon charges and form factors using seven ensembles of $2+1$-flavor Wilson-clover fermions. The axial vector and pseudoscalar form factors obtained on each of these ensembles satisfy the partially conserved axial current relation between them once the lowest energy $N\ensuremath{\pi}$ excited state is included in the spectral decomposition of the correlation functions used for extracting the ground state matrix elements. Similarly, we find evidence that the $N\ensuremath{\pi}\ensuremath{\pi}$ excited state contributes to the correlation functions with the insertion of the vector current, consistent with the vector meson dominance model. The resulting form factors are consistent with the Kelly parametrization of the experimental electric and magnetic data. Our final estimates for the isovector charges are ${g}_{A}^{u\ensuremath{-}d}=1.32(6)(5{)}_{\mathrm{sys}}$, ${g}_{S}^{u\ensuremath{-}d}=1.06(9)(6{)}_{\mathrm{sys}}$, and ${g}_{T}^{u\ensuremath{-}d}=0.97(3)(2{)}_{\mathrm{sys}}$, where the first error is the overall analysis uncertainty and the second is an additional combined systematic uncertainty. The form factors yield: (i) the axial charge radius squared, ${⟨{r}_{A}^{2}⟩}^{u\ensuremath{-}d}=0.428(53)(30{)}_{\mathrm{sys}}\text{ }\text{ }{\mathrm{fm}}^{2}$; (ii) the induced pseudoscalar charge, ${g}_{P}^{*}=7.9(7)(9{)}_{\mathrm{sys}}$; (iii) the pion-nucleon coupling, ${g}_{\ensuremath{\pi}\mathrm{NN}}=12.4(1.2)$; (iv) the electric charge radius squared, ${⟨{r}_{E}^{2}⟩}^{u\ensuremath{-}d}=0.85(12)(19{)}_{\mathrm{sys}}\text{ }\text{ }{\mathrm{fm}}^{2}$; (v) the magnetic charge radius squared, ${⟨{r}_{M}^{2}⟩}^{u\ensuremath{-}d}=\phantom{\rule{0ex}{0ex}}0.71(19)(23{)}_{\mathrm{sys}}\text{ }\text{ }{\mathrm{fm}}^{2}$; and (vi) the magnetic moment, ${\ensuremath{\mu}}^{u\ensuremath{-}d}=4.15(22)(10{)}_{\mathrm{sys}}$. All our results are consistent with phenomenological/experimental values but with larger errors. Last, we present a Pad\'e parametrization of the axial, electric, and magnetic form factors over the range $0.04<{Q}^{2}<1\text{ }\text{ }{\mathrm{GeV}}^{2}$ for phenomenological studies.

Determination of the generalized parton distributions through the analysis of the world electron scattering data considering two-photon exchange corrections

We determine the valence generalized parton distributions (GPDs) $ H_v^q $ and $ E_v^q $ with their uncertainties at zero skewness by performing a $ \chi^2 $ analysis of the world electron scattering data considering two-photon exchange corrections. The data include a wide and updated range of the electric and magnetic form factors (FFs) of the proton and neutron. As a result, we find that there are no enough constraints on GPDs $ E_v^q $ from FFs data solely though $ H_v^q $ are well constrained. By including the new data of the charge and magnetic radius of the nucleon in the analysis, we show that they put new constraints on the final GPDs, especially on $ E_v^q $. Moreover, we calculate the gravitational FF $ M_2 $ and the total angular momentum $ J^q $ using the extracted GPDs and compare them with the FFs obtained from the light-cone QCD sum rules (LCSR) and Lattice QCD. We show that our results are interestingly in a good consistency with the pure theoretical predictions.

Transverse charge density and the radius of the proton

A puzzling discrepancy exists between the values of the proton charge radius obtained using different experimental techniques: elastic electron-proton scattering and spectroscopy of electronic and muonic hydrogen. The proton radius is defined through the slope of the electric form factor, $G_E(Q^2)$, at zero four-momentum transfer, which is inaccessible in scattering experiments. We propose a novel method for extracting the proton radius from scattering data over a broad $Q^2$ range rather than attempting to directly determine the slope of $G_E$ at $Q^2 = 0$. This method relates the radius of the proton to its transverse charge density, which is the two-dimensional Fourier transform of the Dirac form factor, $F_1(Q^2)$. We apply our method to reanalyze the extensive data obtained by the A1 Collaboration [J. C. Bernauer et al., Phys. Rev. Lett. 105, 242001 (2010)] and extract a radius value, $r_E = 0.889(5)_{\text{stat}}(5)_{\text{syst}}(4)_{\text{model}}~\text{fm}$, that is consistent with the original result. We also provide new parametrizations for the Dirac and Pauli form factors and the transverse charge and magnetization densities of the proton. Our reanalysis shows that the proton radius discrepancy cannot be explained by issues with fitting and extrapolating the A1 data to $Q^2 = 0$.