Electron-proton Cross Section Research Articles

Baryonic dark forces in electron-beam fixed-target experiments

New GeV-scale dark forces coupling predominantly to quarks offer novel signatures that can be produced directly and searched for at high-luminosity colliders. We compute the photon-proton and electron-proton cross sections for producing a GeV-scale gauge boson arising from a U(1)B gauge symmetry. Our calculation relies on vector meson dominance and a phenomenological model for diffractive scattering used for vector-meson photoproduction. The parameters of our phenomenological model are fixed by performing a Markov Chain Monte Carlo fit to existing exclusive photoproduction data for ω and ϕ mesons. Our approach can be generalized to other GeV-scale dark gauge forces.

Measurement of R=σL/σT and the separated longitudinal and transverse structure functions in the nucleon-resonance region

We report on a detailed study of longitudinal strength in the nucleon resonance region, presenting new results from inclusive electron-proton cross sections measured at Jefferson Lab Hall C in the four-momentum transfer range 0.2<Q2<5.5GeV2. The data have been used to accurately perform 167 Rosenbluth-type longitudinal/transverse separations. The precision R=σL/σT data are presented here, along with the first separate values of the inelastic structure functions F1 and FL in this regime. The resonance longitudinal component is found to be significant, both in magnitude and in the existence of defined mass peaks. Additionally, quark-hadron duality is here observed above Q2=1GeV2 in the separated structure functions independently.Received 15 December 2021Accepted 9 June 2022DOI:https://doi.org/10.1103/PhysRevC.105.065205©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear structure & decaysNuclear Physics

Low-mass Diffraction Dissociation at the LHC. Role of the Background

A dual model with a nonlinear proton Regge trajectory in the missing mass (M2X) channel is constructed. A background based on a direct-channel exotic trajectory, developed and applied earlier for the inclusive electron-proton cross section description in the nucleon resonance region, is used. The parameters of the model are determined from the extrapolations to earlier experiments. Predictions for the low-mass (2 &lt; M2X &lt; 8 GeV2) diffraction dissociation cross sections at the LHC energies are given.

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.

Sensitivity of the elastic electron–proton cross section to the proton radius

The precise determination of the proton radius from recent elastic scattering electron–proton data is discussed. The necessary precision on the elastic cross section to discriminate among the values coming from atomic spectroscopy is scrutinized in terms of the relevant quantity, i.e., the derivative of the form factor. It is shown that its uncertainty is two orders of magnitude larger that the error on the cross section, that is the measured observable. Different fits of the available data and of their discrete derivative, with analytical constraints are shown. The systematic error associated to the radius is evaluated taking into account the uncertainties from different sources, as the extrapolation to the static point, the choice of the class of fitting functions and the range of the data sample. This error is shown to be also orders of magnitude larger than commonly assumed.

Two-Photon Exchange: Future Experimental Prospects

The proton elastic form factor ratio is accessible in unpolarized Rosenbluth-type experiments as well as experiments which make use of polarization degrees of freedom. The extracted values show a distinct discrepancy, growing with $Q^2$. Three recent experiments tested the proposed explanation, two-photon exchange, by measuring the positron-proton to electron-proton cross section ratio. In the results, a small two-photon exchange effect is visible, significantly different from theoretical calculation. Theory at larger momentum transfer remains untested. This paper discusses the possibilities for future measurements at larger momentum transfer.

Constraints on the virtual Compton scattering on the nucleon in a new dispersive formalism

The dispersive representation of the virtual Compton forward scattering amplitude has been recently reexamined in connection with the evaluation of the Cottingham formula for the proton-neutron electromagnetic mass difference. The most difficult part of the analysis is related to one of the invariant amplitudes, denoted as $T_1(\nu, Q^2)$, which requires a subtraction in the standard dispersion relation with respect to the energy $\nu$ at fixed photon momentum squared $q^2=-Q^2$. We propose an alternative dispersive framework, which implements analyticity and unitarity by combining the Cauchy integral relation at low and moderate energies with the modulus representation of the amplitude at high energies. Using techniques of functional analysis, we derive a necessary and sufficient condition for the consistency with analyticity of the subtraction function $S_1(Q^2)=T_1(0, Q^2)$, the electron-proton cross sections measured at low and moderate energies and the Regge model assumed to be valid at high energies. From this condition we obtain model-independent constraints on the subtraction function, confronting them with the available information on nucleon magnetic polarizabilities and results reported recently in the literature. The formalism can be used also for testing the existence of a fixed pole at $J=0$ in the angular momentum plane, but more accurate data are necessary for a definite answer.

Factorization breaking in diffraction

The measurements of diffractive dijet and open charm electron–proton cross-sections in deep-inelastic scattering (DIS) and photoproduction at HERA are discussed with an emphasis on possible quantum chromodynamics (QCD) factorization breaking.

Towards a resolution of the proton form factor problem: new electron and positron scattering data.

There is a significant discrepancy between the values of the proton electric form factor, G(E)(p), extracted using unpolarized and polarized electron scattering. Calculations predict that small two-photon exchange (TPE) contributions can significantly affect the extraction of G(E)(p) from the unpolarized electron-proton cross sections. We determined the TPE contribution by measuring the ratio of positron-proton to electron-proton elastic scattering cross sections using a simultaneous, tertiary electron-positron beam incident on a liquid hydrogen target and detecting the scattered particles in the Jefferson Lab CLAS detector. This novel technique allowed us to cover a wide range in virtual photon polarization (ϵ) and momentum transfer (Q(2)) simultaneously, as well as to cancel luminosity-related systematic errors. The cross section ratio increases with decreasing ϵ at Q(2)=1.45 GeV(2). This measurement is consistent with the size of the form factor discrepancy at Q(2)≈1.75 GeV(2) and with hadronic calculations including nucleon and Δ intermediate states, which have been shown to resolve the discrepancy up to 2-3 GeV(2).

EM Form Factors and OLYMPUS

The elastic form factors of the nucleon characterize the distributions of charge and magnetization in momentum space and are important input for calculations of strong interaction phenomena and nuclear structure. The dramatic discrepancy in the observed ratio of elastic proton form factors between the Rosenbluth separation and polarization transfer methods has invoked numerous theoretical and experimental investigations. The previously neglected effect from two-photon exchange has become the favored explana- tion for the discrepancy. While the effect can not be calculated from first principles, it can be verified experimentally in several ways, most stringently by comparing the positron- proton and electron-proton elastic cross sections. The OLYMPUS experiment at DESY has been carried out to quantify the effect of two-photon exchange using intense stored positron and electron beams along with an internal unpolarized hydrogen target and a large acceptance detector to measure the ratio of the positron-proton and electron-proton elastic scattering cross sections. The status of proton form factor measurements and of the experimental efforts to verify the effect of two-photon exchange is presented, with some emphasis on the OLYMPUS experiment.

Empirical fit to precision inclusive electron-proton cross sections in the resonance region

An empirical fit is described to measurements of inclusive inelastic electron-proton cross sections in the kinematic range of four-momentum transfer $0\ensuremath{\leqslant}{Q}^{2}&lt;8$ GeV${}^{2}$ and final-state invariant mass $1.1&lt;W&lt;3.1$ GeV. The fit is constrained by the recent high-precision longitudinal and transverse separated cross section measurements from Jefferson Lab Hall C, unseparated Hall C measurements up to ${Q}^{2}$ $\ensuremath{\approx}7.5$ ${\mathrm{GeV}}^{2}$, and photoproduction data at ${Q}^{2}=0$. Compared to previous fits, the present fit covers a wider kinematic range, fits both transverse and longitudinal cross sections, and features smooth transitions to the photoproduction data at ${Q}^{2}=0$ and deep inelastic scattering data at high ${Q}^{2}$ and $W$.

Perturbative QCD predictions for two-photon exchange

We study two-photon exchange (TPE) in the elastic electron-nucleon scattering at high ${Q}^{2}$ in the framework of perturbative quantum chromodynamics. The obtained TPE amplitude is of order $\ensuremath{\alpha}/{\ensuremath{\alpha}}_{s}$ with respect to Born approximation. Its shape and value are sensitive to the choice of nucleon wave function, thus study of TPE effects can provide important information about nucleon structure. With the wave functions based on quantum chromodynamics sum rules, TPE correction to the electron-proton cross section has a negative sign, is almost linear in $\ensuremath{\epsilon}$, and grows logarithmically with ${Q}^{2}$ up to 7% at ${Q}^{2}=30\text{ }\text{ }{\mathrm{GeV}}^{2}$. The results of existing hadronic calculations, taking into account just the nucleon intermediate state, can be smoothly connected with the perturbative quantum chromodynamics result near ${Q}^{2}\ensuremath{\sim}3\text{ }\text{ }{\mathrm{GeV}}^{2}$. Above this point two methods disagree, which implies that the hadronic approach becomes inadequate at high ${Q}^{2}$. Other relevant observables, such as the electron/positron cross section ratio, are also discussed.

Implications of the discrepancy between proton form factor measurements

Recent polarization transfer measurements of the proton electromagnetic form factors yield very different results from previous Rosenbluth extractions. This inconsistency implies uncertainties in our knowledge of the form factors and raises questions about how to best combine data from these two techniques. If the discrepancy is due to missing correction to the cross section data, as has been suggested, then different applications will require the use of different form factors. We present two extractions of the form factors: a global fit to the world's cross section data, and a combined extraction from polarization transfer and cross section data. The former provides a parametrization of the elastic electron-proton cross section, while the latter provides a consistent extraction of the underlying form factors, under the assumption that missing terms in the radiative correction explain the difference between the cross section and polarization transfer results.

Kinematically complete analysis of the CLAS data on the proton structure functionF2in a Regge-dual model

The recently measured inclusive electron-proton cross section in the nucleon resonance region, performed with the CLAS detector at the Thomas Jefferson Laboratory, has provided new data for the nucleon structure function $F_2$ with previously unavailable precision. In this paper we propose a description of these experimental data based on a Regge-dual model for $F_2$. The basic inputs in the model are nonlinear complex Regge trajectories producing both isobar resonances and a smooth background. The model is tested against the experimental data, and the $Q^2-$ dependence of the moments is calculated. The fitted model for the structure function (inclusive cross section) is a limiting case of the more general scattering amplitude equally applicable to deeply virtual Compton scattering (DVCS). The connection between the two is discussed.

Kinematically complete measurement of the proton structure functionF2in the resonance region and evaluation of its moments

We measured the inclusive electron-proton cross section in the nucleon resonance region (W < 2.5 GeV) at momentum transfers Q**2 below 4.5 (GeV/c)**2 with the CLAS detector. The large acceptance of CLAS allowed for the first time the measurement of the cross section in a large, contiguous two-dimensional range of Q**2 and x, making it possible to perform an integration of the data at fixed Q**2 over the whole significant x-interval. From these data we extracted the structure function F2 and, by including other world data, we studied the Q**2 evolution of its moments, Mn(Q**2), in order to estimate higher twist contributions. The small statistical and systematic uncertainties of the CLAS data allow a precise extraction of the higher twists and demand significant improvements in theoretical predictions for a meaningful comparison with new experimental results.

Unfactorized versus factorized calculations for2H(e,e′p)reactions at GeV energies

In the literature, one often finds calculations of ${(e,e}^{\ensuremath{'}}p)$ reactions at GeV energies using the factorization approach. Factorization implies that the differential cross section can be written as the product of an off-shell electron-proton cross section and a distorted missing momentum distribution. While this factorization appears in the nonrelativistic plane wave impulse approximation, it is broken in a more realistic approach. The main source of factorization breaking is final state interactions. In this paper, sources of factorization breaking are identified and their numerical relevance is examined in the reaction ${}^{2}\mathrm{H}{(e,e}^{\ensuremath{'}}p)$ for various kinematic settings in the GeV regime. The results imply that factorization should not be used for precision calculations, especially as unfactorized calculations are available.

Structure of the6Li→p+(nα) vertex:Li6(e,e’p)nαreaction

Three-body models of $^{6}\mathrm{Li}$ are used to describe the reaction $^{6}\mathrm{Li}$(e,e'p)n\ensuremath{\alpha}. Under the impulse approximation, the differential cross section for the $^{6}\mathrm{Li}$(e,e'p)n\ensuremath{\alpha} reaction with unpolarized particles factorizes into a product of a kinematical factor, the (off-shell) electron-proton cross section, and a distorted spectral function of the ejected proton in the $^{6}\mathrm{Li}$ nucleus. A prescription by De Forest is used to carry the ep cross section off the proton mass shell. The spectral function, containing all of the nuclear physics in the reaction, is found from the $^{6}$Li\ensuremath{\rightarrow}p+(n\ensuremath{\alpha}) vertex amplitude. A unified theoretical description of both the bound state and the (n\ensuremath{\alpha}) scattering state is employed to predict the $^{6}$Li\ensuremath{\rightarrow}p+(n\ensuremath{\alpha}) vertex amplitude. For (n\ensuremath{\alpha}) relative energies below 16 MeV and proton momenta below 200 MeV/c, the ${P}_{3/2}$ \ensuremath{\alpha}N resonance dominates the shape of the spectral function. However, the contribution of the outgoing scattering wave due to the ${S}_{1/2}$ \ensuremath{\alpha}N interaction has a significant role for momenta of the (n\ensuremath{\alpha}) pair below 40 MeV/c, making the 2s orbitals in $^{6}\mathrm{Li}$ control the behavior of the momentum distribution near zero momentum transfer to the (n\ensuremath{\alpha}) pair. Recent coincidence experiments give good agreement with theory. Experimental resolutions are currently not quite capable of discriminating between various ${S}_{1/2}$ \ensuremath{\alpha}N interactions used in the three-body calculation.

Absolute electron-proton cross sections at low momentum transfer measured with a high pressure gas target system

Absolute differential cross sections for elastic electron-proton scattering have been measured in a four-momentum transfer range up to 1.4 fm −2. Using a high pressure gas target system, we have obtained highly accurate data with a small normalization error of 0.5%. The electromagnetic form factors G E and G M have been extracted and the rms charge radius has been determined to be 〈r 2 E 〉 p 1 2 = 0.862±0.012 fm . The shape of the isovector spectral function near threshold shows a significant non-resonant contribution of the two-pion state. This enhancement is so strong that the derivative at q 2 = 0 differs considerably from the usual vector meson dominance model value. This result is in good agreement with theoretical predictions.

Comparison of Muon-Proton and Electron-Proton Inelastic Scattering

Measurements of the differential cross section for the inelastic scattering of 12-GeV/c muons on protons are reported. These measurements cover a kinematic range of $|{q}^{2}|$ (the square of the four-momentum transferred from the lepton) up to 4.0 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ and of muon energy losses ($\ensuremath{\nu}$) up to 9.0 GeV. Only the scattered muon is observed in an optical spark-chamber apparatus. The data are compared with electron-proton inelastic scattering, and analyzed in terms of possible lepton form factors and anomalous interactions. $\ensuremath{\mu}\ensuremath{-}p$ inelastic scattering is found to exhibit the same mild $|{q}^{2}|$ behavior as does $e\ensuremath{-}p$ inelastic scattering. No experimentally significant deviation from the predictions of muon-electron universality has been found. If the ratio of muon to electron inelastic cross sections is parametrized by the form ${(1.0+\frac{|{q}^{2}|}{\ensuremath{\Lambda}_{D}^{}{}_{}{}^{2}})}^{\ensuremath{-}2}$, we find with 97.7% confidence that ${\ensuremath{\Lambda}}_{D}g4.1$ GeV/c. The muon-proton cross sections on the average are slightly smaller than the electron-proton cross sections. This observation is not experimentally significant because such a difference might be caused by systematic errors, but this observation is used to speculate as to the most fruitful direction for future experiments.

Electroproduction and Photoproduction—Some Gross Characteristics at Extreme Energies

Certain gross characteristics of inelastic lepton-hadron and photon-hadron collisions at extreme energies are correlated and discussed. It is argued that the total inelastic electron-proton cross section, for example, increases like ${\mathrm{ln}}^{2}E$ as $E\ensuremath{\rightarrow}\ensuremath{\infty}$, where $E$ is the incident electron energy, if the total photoabsorption cross section tends to a nonzero limit at high energies. The behavior of partial cross sections and average multiplicities for a given secondary at extreme energies for the two kinds of processes are also discussed. In particular, it is shown that if the behavior of the average multiplicity of any given hadron with respect to the incident energy is the same in electroproduction and photoproduction processes, it could only be logarithmic (or powers thereof). Implications of the various results in the context of certain existing models are also discussed.