Magnetic Form Factors Of Proton Research Articles

Generalized parton distributions at zero skewness

We present a new determination of the generalized parton distributions (GPDs) with their uncertainties at zero skewness, $ \xi =0 $, through a simultaneous analysis of all available experimental data of the nucleon electromagnetic form factors (FFs), nucleon charge and magnetic radii, proton axial FFs (AFFs) and wide-angle Compton scattering (WACS) cross sections for the first time, and we investigate whether there is any tension between these data. This can be considered the most comprehensive analysis of GPDs at $ \xi=0 $ performed so far. We show that such an analysis provides the simultaneous determination of three kinds of GPDs, namely $ H^q $, $ \widetilde{H}^q $ and $ E^q $, considering also the sea-quark contributions. As a result, we find that the inclusion of the WACS and AFF data at larger values of the momentum transfer squared $ Q^2=-t $ can put new constraints on GPDs and change them drastically in some cases. We show that there is a considerable tension between the WACS and the proton magnetic form factor ($ G_M^p $) data, especially at larger values of $ -t $. However, we indicate that the results for the gravitational FF $ M_2 $ and the proton total angular momentum $ J^p $ calculated using the extracted GPDs are in relatively good agreement with the light-cone QCD sum rules (LCSRs) and lattice QCD predictions when the sea-quark contributions are considered and both WACS and $ G_M^p $ data are included in the analyses simultaneously.

Form Factors and Two-Photon Exchange in High-Energy Elastic Electron-Proton Scattering.

We present new precision measurements of the elastic electron-proton scattering cross section for momentum transfer (Q^{2}) up to 15.75 (GeV/c)^{2}. Combined with existing data, these provide an improved extraction of the proton magnetic form factor at high Q^{2} and double the range over which a longitudinal or transverse separation of the cross section can be performed. The difference between our results and polarization data agrees with that observed at lower Q^{2} and attributed to hard two-photon exchange (TPE) effects, extending to 8 (GeV/c)^{2} the range of Q^{2} for which a discrepancy is established at >95% confidence. We use the discrepancy to quantify the size of TPE contributions needed to explain the cross section at high Q^{2}.

Pauli Radius of the ProtonSupported by the National Natural Science Foundation of China (Grant Nos. 12135007 and 11805097), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20180323), and STRONG-2020, “the strong interaction at the frontier of knowledge: fundamental research and applications” which received funding from the European Union’s Horizon 2020 Research and Innovation Programme (Grant No. 824093).

Using a procedure based on interpolation via continued fractions supplemented by statistical sampling, we analyze proton magnetic form factor data obtained via electron+proton scattering on Q 2 ∈ [0.027, 0.55] GeV2 with the goal of determining the proton magnetic radius. The approach avoids assumptions about the function form used for data interpolation and ensuing extrapolation onto Q 2 ≃ 0 for extraction of the form factor slope. In this way, we find r M = 0.817(27) fm. Regarding the difference between proton electric and magnetic radii calculated in this way, extant data are seen to be compatible with the possibility that the slopes of the proton Dirac and Pauli form factors, F 1,2(Q 2), are not truly independent observables; to wit, the difference , viz., the proton Foldy term.

A measurement of two-photon exchange in Super-Rosenbluth separations with positron beams

The proton electric and magnetic form factors, $G_E$ and $G_M$, are intrinsically connected to the spatial distribution of charge and magnetization in the proton. For decades, Rosenbluth separation measurements of the angular dependence of elastic e$^-$-p scattering were used to extract $G_E$ and $G_M$. More recently, polarized electron scattering measurements, aiming to improve the precision of $G_E$ extractions, showed significant disagreement with Rosenbluth measurements at large momentum transfers ($Q^2$). This discrepancy is generally attributed to neglected two-photon exchange (TPE) corrections. At larger $Q^2$ values, a new `Super-Rosenbluth' technique was used to improve the precision of the Rosenbluth extraction, allowing for a better quantification of the discrepancy, while comparisons of e$^+$-p and e$^-$-p scattering indicated the presence of TPE corrections, but at $Q^2$ values below where a clear discrepancy is observed. In this work, we demonstrate the significant benefits to combining the Super-Rosenbluth technique with positron beam measurements. This approach provides a greater kinematic reach and is insensitive to some of the key systematic uncertainties in previous positron measurements.

Calculations of the deuteron form factors

On the received coefficients of the analytical forms for deuteron wave function in coordinate representation in form r^(l+1)*exp(-A*r) for the modern realistic nucleon-nucleon potentials NijmI, NijmII, Nijm93, Reid93 and Argonne v18 are calculated charge GC(p), quadrupole GQ(p) and magnetic GM(p) deuteron form factors. An original dipole fit for proton and neutron isoscalar electric and magnetic form factors is used for calculations. Theoretical calculations of values of the deuteron form factor are compared with their experimental data of world collaborations (Bates, BLAST, Bonn, JLab, Mainz, Naval Research Lab, NIKHEF, Orsay, Saclay, SLAC, Stanford, VEPP3 and VEPP4) and reviews (Abbott, Boden, Garcon and Karpius). The change of the sign of form factors is in the pulse regions at 4.7-4.9 fm-1 for GC; at 12.8-14.7 fm-1 for GQ; at 6.3-8.1 and 11.4-12.2 fm-1 for GM. The theoretical values for the form factors GQ(0) and GM(0) were calculated at the boundary condition for the momentum at p2=0. Calculated positions of the zero for deuteron form factors are compared with values for other potential models. The peculiarities of parametrizations of deuteron form factors for theoretical approaches and fits of theoretical calculations to experimental values, which are described in the cited literature, are analyzed. Formulas for spherical and quadrupole form factors are writed, which are expressed in terms of the coefficients for the indicated deuteron wave function. At large values of momentum the asymptotics of the deuteron form factors are determined by the coefficients of the analytical forms for deuteron wave function, nucleon isoscalar form factors and the order of momentum in the denominator. The further use of deuteron form factors for obtaining polarization observables in processes involving deuteron as a projectile is discussed.

EFFECTS OF SCALAR BOSON IN ELASTIC PROTON-ELECTRON SCATTERING

The differential cross section for the elastic scattering of unpolarized protons on unpolarized electrons at rest is calculated taking into account two mechanisms: one-photon and scalar-boson exchange. The spin correlation coefficients, when the proton beam and the electron target are both arbitrarily polarized, have also been calculated. These observables are calculated in terms of the proton electromagnetic form factors, namely magnetic and electric ones. Some peculiarities of the inverse kinematics (the mass of the colliding particle is larger than mass of the target particle) have been discussed. It was shown that all the spin correlation coefficients in the elastic proton electron collisions are proportional to the proton magnetic form factor. The same behaviour takes place for the spin correlation coefficients in the elastic electron proton scattering (the electron beam and proton target are both polarized). It was shown that only the interference of the two mechanisms (one-photon and one-boson) gives nonzero contribution to the spin correlation coefficients. If the spin vectors of the proton beam and electron target lie in the reaction plane then the corresponding spin correlation coefficients are zero for the case when scattered electron momentum is in the direction of the proton beam momentum.

Measurement of the proton and kaon time-like electromagnetic form factors at high energy with the BaBar detector

We have used ISR technique to measure the proton magnetic form factor in the energy region from 3.0 to 6.5 GeV and charged kaon form factor in the range from 2.6 to 7.5 GeV. The proton data clearly indicate that the difference between values of time- and space-like magnetic form factors decreases with increase of energy. The kaon form factor decreases with energy faster than 1/E2, approaching the asymptotic pQCD predictions.

On higher order radiative corrections to elastic electron–proton scattering

QED radiative corrections to elastic electron-proton scattering at low energies are discussed. Corrections to the electron line and effects due to vacuum polarization are computed. Higher order effects are estimated for the conditions of the experiment on the electric and magnetic proton form factors by A1 Collaboration. Calculations are performed within the next-to-leading approximation. Inclusion of the higher order effects can affect the value of the proton charge radius extracted from the experimental data.

Flavor decomposition of the nucleon electromagnetic form factors at lowQ2

Background: The spatial distribution of charge and magnetization within the proton is encoded in the elastic form factors. These have been precisely measured in elastic electron scattering, and the combination of proton and neutron form factors allows for the separation of the up- and down-quark contributions.Purpose: In this work, we extract the proton and neutron form factors from worldwide data with an emphasis on precise new data covering the low-momentum region, which is sensitive to the large-scale structure of the nucleon. From these, we separate the up- and down-quark contributions to the proton form factors.Method: We combine cross section and polarization measurements of elastic electron-proton scattering to separate the proton form factors and two-photon exchange (TPE) contributions. We combine the proton form factors with parametrization of the neutron form factor data and uncertainties to separate the up- and down-quark contributions to the proton's charge and magnetic form factors.Results: The extracted TPE corrections are compared to previous phenomenological extractions, TPE calculations, and direct measurements from the comparison of electron and positron scattering. The flavor-separated form factors are extracted and compared to models of the nucleon structure.Conclusions: With the inclusion of the precise new data, the extracted TPE contributions show a clear change of sign at low ${Q}^{2}$, which is necessary to explain the high-${Q}^{2}$ form factor discrepancy while being consistent with the known ${Q}^{2}\ensuremath{\rightarrow}0$ limit. We find that the new Mainz data yield a significantly different result for the proton magnetic form factor and its flavor-separated contributions. We also observe that the rms radius of both the up- and down-quark distributions are smaller than the rms charge radius of the proton.

Nucleon form factors and final state radiative corrections toe+e−→p¯pγ

New parametrisation for the electric and the magnetic form factors of proton and neutron are presented. The proton form factors describe well the recent measurements by BaBar collaboration and earlier ones of the ratio of the form factors in space-like region. The neutron form factors are consistent with earlier measurements of neutron pair production and ratio of the form factors in the space-like region. These form factors are implemented into the generator PHOKHARA, which simulates the reactions $e^+e^-\to \bar p p \gamma$ and $e^+e^-\to \bar n n\gamma$. The influence of final state radiation is investigated.

Nucleon magnetic form factors with non-local chiral effective Lagrangian

Chiral perturbation theory is a powerful method to investigate the hadron properties. We apply the non-local chiral effective Lagrangian to study nucleon magnetic form factors. The octet and decuplet intermediate states are included in the one loop calculation. With the modified propagators and non-local interactions, the loop integral is convergent. The obtained proton and neutron magnetic form factors are both reasonable up to relatively large $Q^2$.

Measurement of thee+e−→pp¯cross section in the energy range from 3.0 to 6.5 GeV

The e+ e- --> p anti-p cross section and the proton magnetic form factor have been measured in the center-of-mass energy range from 3.0 to 6.5 GeV using the initial-state-radiation technique with an undetected photon. This is the first measurement of the form factor at energies higher than 4.5 GeV. The analysis is based on 469 fb-1 of integrated luminosity collected with the BABAR detector at the PEP-II collider at e+e- center-of-mass energies near 10.6 GeV. The branching fractions for the decays J/psi --> p anti-p and psi(2S) --> p anti-p have also been measured.

Low-Q: proton electric and magnetic form factors

An extensive measurement of the elastic H(e,e’)p reaction in the Q2-region from 0.003 to 1 (GeV/c)2 has been performed with the three-spectrometer set-up of the A1 collaboration at the Mainz Microtron. The data set consists of about 3,000 overlapping cross-section measurements with a high level of internal redundancy, which allow for a determination of the electric and magnetic form factors with strict control over statistical and systematic errors, in particular also of the charge and magnetization radii of the proton. Besides the classical Rosenbluth separation, the form factors are separated by direct, global fits of different sufficiently flexible models.

Exact results in QED

This review is devoted to exact calculations of cross sections of QED processes in relativistic approach. We consider the case when the velocity of final heavy particles are not particularly close to the speed of light. Especially the cases of muon radiative pair creation is considered. In frames of QED with pion form-factor we estimate the pion radiative pair creation. All leading terms are included in the frames of structure function approach. The annihilation of electron-positron to the hadronic final state with one additional tagged photon is considered. The radiative corrections are calculated and the numerical estimation is made. Target spin asymmetry and charge asymmetry are investigated for eμ scattering processes. Initial state radiation (returning to resonance) mechanism is investigated including radiative corrections to initial and final states. Possible method of experimental extraction of the ratio of electric and magnetic form-factors of proton is suggested for different processes in lepton proton scattering. Some useful algebraic relations and integrals are presented.

HighQ2behavior of the electromagnetic form factors in the relativistic hypercentral constituent quark model

The ratio $R_p$ between the electric and magnetic proton form factors has been recently measured at JLab up to $Q^2=8.5 ~GeV^2$. We have extended the calculation of the nucleon form factors with the hypercentral Constituent Quark Model and compared them with the data on $R_p$ and on the $Q^2$ behavior of the ratio $Q^2 F_2/F_1$. In both cases the theoretical curves agree with the experimental points.

Nucleon form factors: the space-time connection

Analyticity of nucleon form factors allows to derive sum rules which, using space-like and time-like data as input, can give unique information about behaviors in energy regions not experimentally accessible. Taking advantage from new time-like data on proton-antiproton differential cross section and hence the possibility to separate electric and magnetic form factors also in the time-like region, we verify the consistency of the asymptotic behavior predicted by the perturbative QCD for the proton magnetic form factor.

Feasibility studies of the time-like proton electromagnetic form factor measurements with $ \overline{{P}}$ANDA at FAIR

The possibility of measuring the proton electromagnetic form factors in the time-like region at FAIR with the \( \overline{{P}}\)ANDA detector is discussed. Detailed simulations on signal efficiency for the annihilation of \( \bar{{p}}\) + p into a lepton pair as well as for the most important background channels have been performed. It is shown that precise measurements of the differential cross-section of the reaction \( \bar{{p}}\) + p \( \rightarrow\) e - + e + can be obtained in a wide kinematical range. The determination of the ratio R of the moduli of the electric and magnetic proton form factors will be possible up to a value of momentum transfer squared of q 2 ≃ 14 (GeV/c)^2 with absolute precision from 0.01 to 0.5 (for R ∼ 1 . The total \( \bar{{p}}\) + p \( \rightarrow\) e - + e + cross-section will be measured up to q 2 ≃ 28 (GeV/c)^2. The results obtained from simulated events are compared to the existing data. Sensitivity to the two-photon exchange mechanism is also investigated.

Time-like proton form factor measurement with P̄ANDA

The electromagnetic probe is an excellent tool to investigate the structure of the nucleon. The nearly 4π detector PANDA, will allow to make a precise determination of the electromagnetic form factors of the proton in the time-like region with unprecedented precision. In the one-photon exchange approximation, the center of mass unpolarized differential cross section of the reaction p̄p → e+e− is a linear combination of the squared moduli of the electric GE and magnetic GM proton form factors. The precise measurement of the angular distribution over almost full angular range then directly gives these quantities. At present only two experiments have provided the ratio R = |GE|/|GM| but with large statistical uncertainties. It is shown that with strict PID cuts and a kinematic fit, the dominant background, p̄p → π+π−, can be supressed to much less than 1% of the signal, without affecting the extraction of the ratio R. P̄ANDA will therefore offer a unique opportunity to measure the ratio with a precision ranging from <1% at low q2 up to 30% for q2 = 14 (GeV/c)2.

The E835 experiment at Fermilab

The resonant formation of charmonium states in \({\overline{p}p}\) annihilations has been studied at Fermilab by the E835 experiment, which has taken data from October 1996 through September 1997 and, in a second run, from January through November 2000. In this talk we will review the most significant physics results of E835 concerning the masses and widths of the charmonium states. We will present a new, high-precision measurement of the ψ(2S) total width. Furthermore we will present a measurement of the proton magnetic form factor in the timelike region.

Strange magnetic form factor of the proton atQ2=0.23 GeV2

We determine the $u$ and $d$ quark contributions to the proton magnetic form factor at finite momentum transfer by applying chiral corrections to quenched lattice data. Heavy baryon chiral perturbation theory is applied at next-to-leading order in the quenched and full QCD cases for the valence sector using finite range regularization. Under the assumption of charge symmetry these values can be combined with the experimental values of the proton and neutron magnetic form factors to deduce a relatively accurate value for the strange magnetic form factor at ${Q}^{2}=0.23 {\mathrm{GeV}}^{2}$, namely, ${G}_{M}^{s}=\ensuremath{-}0.034\ifmmode\pm\else\textpm\fi{}0.021 {\ensuremath{\mu}}_{N}$.