We apply a subtracted dispersion relation (DR) formalism with the aim to improve predictions for the two-photon exchange (TPE) corrections to elastic electron-proton scattering observables at small momentum transfers. We study the formalism on the elastic TPE contribution in comparison with existing data for unpolarized cross sections. We extend the general formalism of TPE to elastic scattering with massive lepton and perform a numerical estimate of the muon-proton scattering at low momentum transfer in view of the upcoming muon-proton scattering experiment (MUSE). We study the influence of the double-virtual Compton scattering (VVCS) subtraction function on the unpolarized lepton-proton scattering cross-section. We show that the resulting TPE correction is negligible in the electron-proton scattering and smaller than planned uncertainties of the MUSE experiment for the subtraction functions evaluated in chiral perturbation theory.
It is suggested that proton elastic scattering on atomic electrons allows a precise measurement of the proton charge radius. Very small values of transferred momenta (up to four order of magnitude smaller than the ones presently available) can be reached with high probability.
The effect of the self-energy on the photon-proton elastic scattering is investigated for the backward and the forward directions. The shape of the Thomson scattering at the photon energy $ω\to 0$ is broken by taking into account the self-energy of proton. The electromagnetic polarizabilities $\barα\pm\barβ$ are calculated by the lowest-order perturbative treatment.
The parity nonconserving longitudinal analyzing power A_L is calculated in elastic pp scattering at the energies below the approximate inelastic region T_lab = 350 MeV. The short-ranged heavy meson rho and omega exchanges as well as the longer-ranged two pion exchanges are considered as the mediators of the parity nonconserving interactions. The DDH "best" coupling values are used as the parity nonconserving meson-NN couplings. Also three different parity nonconserving two-pion exchange potentials by various authors are compared.
Higher-order QED effects play an important role in precision measurements of nucleon elastic form factors in electron scattering. Here we introduce a two-photon exchange QED correction to the parity-violating polarization asymmetry of elastic electron-proton scattering. We calculate this correction in the parton model using the formalism of generalized parton distributions, and demonstrate that it can reach several per cent in certain kinematics, becoming comparable in size with existing experimental measurements of strange-quark effects in the proton neutral weak current.
We calculate $γZ$ exchange corrections to the parity-violating asymmetry of the elastic electron-proton scattering in a parton model using the formalism of generalized parton distributions(GPDs). We also examine the validity of the zero-momentum-transfer approximation adopted in the literatures and find that it overestimates the $γZ$ exchange effect significantly at the forward scattering angles.
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 such precision is two orders of magnitude higher than the precision on the cross section, that is the measured observable. Different fits on the available data and of their discrete derivative, with analytical constraints are shown. The systematic error associa…
We apply a subtracted dispersion relation formalism with the aim to improve predictions for the two-photon exchange corrections to elastic electron-proton scattering observables at finite momentum transfers. We study the formalism on the elastic contribution, and make a detailed comparison with existing data for unpolarized cross sections as well as polarization transfer observables.
We present calculations of the two-pion-exchange contribution to proton-proton scattering at 90 degrees using form factors appropriate for representing the distribution of the constituent partons of the nucleon. Talk given at MENU2001, George Washington University, July 26-31, 2001
Two-photon exchange contributions to elastic electron-proton scattering cross sections are evaluated in a simple hadronic model including the finite size of the proton. The corrections are found to be small in magnitude, but with a strong angular dependence at fixed $Q^2$. This is significant for the Rosenbluth technique for determining the ratio of the electric and magnetic form factors of the proton at high $Q^2$, and partly reconciles the apparent discrepancy with the results of the polarization transfer technique.
We extend the general formalism of two-photon exchange to elastic lepton-nucleon scattering by accounting for all lepton mass terms. We then perform a numerical estimate of the muon-proton scattering at low momentum transfer in view of the future MUSE experiment. For this purpose, we estimate the two-photon exchange corrections to muon-proton scattering observables by considering the contribution of the proton intermediate state, which is expected to dominate at very low momentum transfers. We find that the two-photon exchange effect to the unpolarized muon- proton scattering cross section in …
Here we consider a contribution of Delta(1232) resonance to real photon radiative corrections for elastic $ep$-scattering. The effect is found to be small for past experiments to study unpolarized cross section as well as for the recent VEPP-3 experiment to investigate two-photon exchange effects by precision measurement of $e^\pm p$-scattering cross sections ratio.
The experimental observables for the elastic reaction induced by protons on electrons are calculated in the Born approximation. Model independent expressions are derived for the differential cross section and polarization observables. Numerical estimations are given for spin correlation coefficients, polarization transfer coefficients and depolarization coefficients, in a wide kinematical range. Specific attention is given to the kinematical conditions, i.e., to the specific range of incident energy and transferred momentum.
The charge asymmetry due to higher-order QED corrections in elastic lepton-proton scattering is estimated without employing the ultrarelativistic approximation. Our calculation is performed by generalizing the soft-photon approximation approach suggested by Tsai. Corresponding loop integrals that take a form of Passarino-Veltman scalar three-point functions are calculated analytically without neglecting the mass of the lepton. Our results provide model-independent charge asymmetry predictions for scattering of unpolarized and massive leptons on proton targets. These predictions can be used in …
We evaluate the two-photon exchange (TPE) correction to the unpolarized elastic electron-proton scattering at small momentum transfer $ Q^2 $. We account for the inelastic intermediate states approximating the double virtual Compton scattering by the unpolarized forward virtual Compton scattering. The unpolarized proton structure functions are used as input for the numerical evaluation of the inelastic contribution. Our calculation reproduces the leading terms in the $ Q^2 $ expansion of the TPE correction and goes beyond this approximation by keeping the full $ Q^2 $ dependence of the proton …
The diffraction slope parameter is investigated for elastic proton-proton and proton-antiproton scattering based on the all available experimental data at low momentum transfer values. Energy dependence of the elastic diffraction slopes is approximated by various analytic functions. The expanded "standard" logarithmic approximations allow to describe experimental slopes in all available energy range reasonably. Various approximations differ from each other both in the low energy and very high energy domains. Predictions for diffraction slope parameter are obtained for elastic proton-proton sca…
A reanalysis of unpolarized electron-proton elastic scattering data is done in terms of the electric to magnetic form factor squared ratio. This observable is in principle more robust against experimental correlations and global normalizations. The present analysis shows indeed that it is a useful quantity that contains reliable and coherent information. The comparison with the ratio extracted from the measurement of the longitudinal to transverse polarization of the recoil proton in polarized electron-proton scattering shows that the results are compatible within the experimental errors. Limi…
We study a parity-conserving single-spin beam asymmetry of elastic electron-proton scattering induced by an absorptive part of the two-photon exchange amplitude. It is demonstrated that excitation of inelastic hadronic intermediate states by the consecutive exchange of two photons leads to logarithmic and double-logarithmic enhancement due to contributions of hard collinear quasi-real photons. The asymmetry at small electron scattering angles is expressed in terms of the total photoproduction cross section on the proton, and is predicted to reach the magnitude of 20-30 parts per million. At th…
The Bialas-Bzdak model of elastic proton-proton scattering assumes a purely imaginary forward scattering amplitude, which consequently vanishes at the diffractive minima. We extended the model to arbitrarily large real parts in a way that constraints from unitarity are satisfied. The resulting model is able to describe elastic $pp$ scattering not only at the lower ISR energies but also at $\sqrt{s}=$7 TeV in a statistically acceptable manner, both in the diffractive cone and in the region of the first diffractive minimum. The total cross-section as well as the differential cross-section of ela…
Neutrino proton elastic scattering and polarized deep inelastic spin sum rules provide complementary information about the spin structure of the proton. We outline the two approaches and what they may teach us about the transition from current to constituent quarks in QCD.
The Bialas-Bzdak model of elastic proton-proton scattering assumes a purely imaginary forward scattering amplitude, which consequently vanishes at the diffractive minima. We extended the model to arbitrarily large real parts in a way that constraints from unitarity are satisfied. The resulting model is able to describe elastic $pp$ scattering not only at the lower ISR energies but also at $\sqrt{s}=$7~TeV in a statistically acceptable manner, both in the diffractive cone and in the region of the first diffractive minimum. The total cross-section as well as the differential cross-section of ela…
We propose a new model for a homogeneous description of hadron-hadron and hadron-nucleus collisions, the Gluon Exchange Model, fundamentally based on color octet (gluon) exchange. In proton-proton collisions we provide an exact description of the final state proton and neutron spectrum including the proton diffractive peak. In proton-nucleus reactions we find that the projectile proton diquark cannot survive in more than about half of multiple proton-nucleon processes and consequently must be very frequently disintegrated, leading to long transfers of baryon number over rapidity space.
Leading electroweak corrections play an important role in precision measurements of the strange form factors. We calculate the two-photon-exchange (TPE) and $γZ$-exchange corrections to the parity-violating asymmetry of the elastic electron-proton scattering in a simple hadronic model including the finite size of the proton. We find both can reach a few percent and are comparable in size with the current experimental measurements of strange-quark effects in the proton neutral weak current. The effect of $γZ$-exchange is in general larger than that of TPE, especially at low momentum transfer $Q…
The diffraction slope parameter is investigated for elastic proton-proton and proton-antiproton scattering based on the all available experimental data at intermediate square of momentum transfer in the main. Energy dependence of the elastic diffraction slope is approximated by various analytic functions in a model-independent fashion. The expanded standard logarithmic approximations allow to describe experimental slopes in all available energy range at qualitative level reasonably. Various fitting functions differ from each other both in low energy and very high energy domains. Predictions fo…
The Chou-Yang model based on multiple diffraction theory has already been used by us to predict the characteristics of antiproton-proton elastic scattering at very high energies. But the recent precise data on proton elastic form factor obtained at JLab essentially deviates from the dipole approximation. We have parametrized the data for the form factor. The computations have been made by using the new expression for the form factor. The implications of the new form factor on the characteristics of antiproton-proton elastic scattering at very high energy have been studied.
Using two hopefully reasonable assumptions plus existing data on the analyzing power in high energy proton-proton elastic scattering, we estimate that the hadronic helicity-flip amplitude at $P^2_{\perp}$ of 0.003 (GeV/c)$^2$ is neglible near 300 GeV. This would allow the absolute calibration of a CNI polarimeter.
Independent multiple scattering (`Landshoff') contributions to proton-proton elastic scattering at wide angles are calculated in the quark-diquark model. Results confirm previous observations about the magnitude of these contributions. The use of the quark-diquark model extends the applicability of perturbative QCD calculations down to lower values of momentum transfer substantially.
The elastic neutron form factors $G_{En}$ and $G_{Mn}$ are calculated in a GPD framework using GPDs obtained from fits to proton elastic form factors $G_{Ep}$ and $G_{Mp}$, and isospin symmetry, with no further changes in parameters. The results for $G_{En}$ are in good agreement with existing data, while those for $G_{Mn}$ are fair. The calculations predict the form factors for future measurements at higher $Q^2$.
We evaluate the two-photon exchange (TPE) correction to the muon-proton elastic scattering at small momentum transfer. Besides the elastic (nucleon) intermediate state contribution, which is calculated exactly, we account for the inelastic intermediate states by expressing the TPE process approximately through the forward doubly virtual Compton scattering. The input in our evaluation is given by the unpolarized proton structure functions and by one subtraction function. For the latter, we provide an explicit evaluation based on a Regge fit of high-energy proton structure function data. It is f…
The differential cross-sections are calculated for proton-proton and proton-antiproton elastic scattering using the phenomenological model based on the analytic parameterizations for global scattering parameters (total cross-section and $ρ$ - parameter), crossing symmetry and derivative relations. We confront our model predictions with experimental data in wide range of energy and momentum transfer. The suggested method may be useful for PAX Program (GSI) as well as for high-energy experiments at RHIC and LHC.
Small momentum transfer elastic proton-proton cross-section at high energies is calculated assuming the nucleon composed of two constituents - a quark and a diquark. A comparison to data (described very well up to -t = 2 GeV^2/c) allows to determine some properties of the constituents. While quark turns out fairly small, the diquark appears to be rather large, comparable to the size of the proton.
The predictions of a model which was tuned in 2013 to describe the elastic and diffractive $pp$- and/or $p\bar p$-data at collider energies up to 7 TeV are compared with the new 13 TeV TOTEM results. The possibility of an odd-signature Odderon exchange contribution is discussed.
The explicit procedures are described for reconstruction of the full set of helicity amplitudes in proton-proton and proton-antiproton elastic scattering. The procedures are based on the derivative relations for the helicity amplitudes in s-channel, on the explicit parametrization of the leading spin non flip amplitudes and crossing - symmetry relations. Asymptotic theorems are used for definition of free parameters in derivative relations. We also study the Odderon influence on the helicity amplitude reconstruction. Reconstruction procedures are valid at extremely wide energy domain and broad…
Under the influence of standardly used description of Coulomb-hadronic interference proposed by West and Yennie the protons have been interpreted as transparent objects; elastic events have been interpreted as more central than inelastic ones. It is known that using more general eikonal model the measured elastic data may be interpreted also very differently; elastic processes being more peripheral than inelastic ones. The most ample elastic data set measured at ISR energy of 52.8 GeV have been recently reanalyzed with the help of the eikonal model and new results obtained. The impact of recen…
Small momentum transfer elastic pion-proton cross-section at high energies is calculated assuming the proton is composed of two constituents, a quark and a diquark. We find that it is possible to fit very precisely the data when (i) the pion acts as a single entity (no constituent quark structure) and (ii) the diquark is rather large, comparable to the size of the proton.
The ratio of elastic to total proton cross sections is related to the darkness of the spatial profile of inelastic interactions by a single parameter in the framework of a simple analytical model. Their critical values at LHC energies are discussed. Two possible variants of their asymptotical behavior are described.
Theoretical proposals of scaling laws for the differential elastic scattering cross sections of protons are confronted with experimental data over a wide energy range. Different combinations of the transferred momentum and energy resulting from the solution of the definite partial differential equation are attempted as scaling variables. Reasonable scaling of the differential cross sections in the diffraction cone has been shown for one of these variables. The violation of the geometrical scaling is ascribed to the increase of the proton blackness with energy. The origin of high-t region viola…
Motivated by the present extensive RHIC (BNL) spin program and further PAX project at FAIR, we study the possibility of explicit reconstruction of full set of helicity amplitudes by joint consideration of elastic proton-proton and proton-antiproton scattering. Procedure is based on the derivative relations for the helicity amplitudes, explicit parametrization of the leading spin non-flip amplitudes and crossing - symmetry relations. Some preliminary results are presented for the PAX energies to show the expected magnitudes of the spin dependent observables as a functions of invariant Mandelsta…
We complete the model-independent analysis of the scaling properties of the differential cross section of elastic proton-proton cross sections, including new TOTEM data published in 2022 at $\sqrt{s} = 8$ TeV. We separate the signal and the background region with a new gating method. In the signal region, we find that the statistical significance of Odderon exchange from the combined 7.0 and 8.0 TeV $pp$ data of TOTEM and the 1.96 TeV $p\bar{p}$ data of D0 is at least 7.32$σ$. In the background region, the scaling functions of elastic proton-proton data at 7 and 8 TeV and that of elastic proto…
Using the available cross section and polarization data for elastic electron-proton scattering, we provide an extraction of the two-photon exchange amplitudes at a common value of four-momentum transfer, around Q^2 = 2.5 GeV^2. This analysis also predicts the e^+ p / e^- p elastic scattering cross section ratio, which will be measured by forthcoming experiments.
The magnitude of the double-spin asymmetry A_{NN} in polarized proton elastic scattering is estimated using results from an earlier determination of the spin-flip coupling of the leading Regge poles (cf. T.L.Trueman, Proceedings of the 16th International Spin Physics Symposium SPIN 2004, eds. F. Bradamante et al, World Scientific, 2005.) The required Regge cuts are estimated using the absorptive Regge model. This estimate is then used to determine the sensitivity of experiments at RHIC to the presence of the Odderon.
The TOTEM Collaboration has measured the differential cross section of elastic proton-proton scattering $\mathrm{d}σ/\mathrm{d}|t|$ at $\sqrt{s} = 2.76$, 7, 8, and 13 TeV. It is observed that all $\mathrm{d}σ/\mathrm{d}|t|$ data points vary in the same way as a function of the center-of-mass energy in the so-called "dip" and "bump" regions. These features hint at possible universal properties of elastic scattering. Based on these empirical observations, and taking inspiration from saturation models, we propose a simple scaling law for proton-proton elastic scattering at LHC energies. We find t…
We discuss different models for the spin structure of the nonperturbative pomeron: scalar, vector, and rank-2 symmetric tensor. The ratio of single-helicity-flip to helicity-conserving amplitudes in polarised high-energy proton-proton elastic scattering, known as the complex r_5 parameter, is calculated for these models. We compare our results to experimental data from the STAR experiment. We show that the spin-0 (scalar) pomeron model is clearly excluded by the data, while the vector pomeron is inconsistent with the rules of quantum field theory. The tensor pomeron is found to be perfectly co…
The C-odd amplitude for the elastic $pp$ and $p\bar{p}$ scattering due to the exchange of the QCD odderon proposed by J.Bartels, L.N.Lipatov and G.P. Vacca is calculated with the Fukugita-Kwiecinski proton impact factor. The found amplitude is very small and cannot be felt in the differential cross-sections at 2.76 and 1.96 Tev respectively.
A model independent Levy expansion method is introduced to describe nearly Levy shaped squared moduli of Fourier transforms. We apply this method to precisely characterize the most recent elastic scattering data of proton-proton collisions at $\sqrt{s} = 13$ TeV. The results reveal a substructure of protons, which is found to be significantly larger and darker in high energy proton-proton collisions at the TeV scale, as compared to a rather faint and apparently overlooked sub-structure, that we also identify in elastic proton-proton scattering at the ISR energy range of $\sqrt{s} = 23 - 62$ Ge…
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.
We discuss the theoretical approach and practical algorithms for simulation of radiative events in elastic ep-scattering. A new Monte Carlo generator for real photon emission events in the process of elastic electron-proton scattering is presented. We perform a few consistency checks and present numerical results.
We investigate the scaling properties of elastic scattering data at ISR and LHC energies and find that the significance of an Odderon observation is larger than the discovery threshold of 5$σ$. As an unexpected by-product of these investigations, for certain experimentally relevant cases, we also conjecture the possibility of proton holography with the help of elastic proton-proton scattering.
This paper describes a new multipurpose event generator, ESEPP, which has been developed for the Monte Carlo simulation of unpolarized elastic scattering of charged leptons on protons. The generator takes into account the lowest-order QED radiative corrections to the Rosenbluth cross section including first-order bremsstrahlung without using the soft-photon or ultrarelativistic approximations. ESEPP can be useful for several significant ongoing and planned experiments.
Elastic scattering data gained for proton-proton collisions at high energies are being analyzed at the present practically only with the help of purely phenomenological mathematical models. And the question exists whether in the impact parameter plane the elastic processes may be interpreted as central or peripheral. From realistic point of view the peripherality should be preferred and one may expect that nucleon dimensions should manifest in some way in elastic data. It will be demonstrated that the elastic pp data at the energy of 53 GeV in the interval |t| from (0., 4.) [GeV^2] may be inte…
A recent Schwinger Generating Functional based formulation, by H.M.Fried,Y.Gabellini,T.Grandou and Y-M.Sheu and P.H.Tsang provided gauge-invariant, exact, non-perturbative solutions for QCD. After choosing a renormalization scheme and assuming a simpler 2 body quark-quark scattering problem, this formalism is tested against experimental elastic proton-proton scattering at LHC energies (7, 8, 13 TeV). This formulation was previously compared with ISR energies at (23.5 - 62.5 GeV). The full scattering amplitude with infinite gluons summed, infinite loops summed and their interference terms are n…
We present a bound on the imaginary part of the single helicity-flip amplitude for spin 1/2-spin 1/2 scattering at small momentum transfer. The variational method of Lagrange multipliers is employed to optimize the single-flip amplitude using the values of the total cross section, the elastic cross section and diffraction slope as equality constraints in addition to the inequality constraints resulting from unitarity. Such bounds provide important information related to the determination of polarization of a proton beam. In the case of elastic proton collisions the analyzing power at small sca…
The measurement of the total $pp$ cross section and its various sub-components (elastic, inelastic and diffractive) is a very powerful tool to understand the proton macro structure and fundamental QCD dynamics. In this contribution I first provide a theoretical introduction to the topic, then a summary of the experimental techniques and finally I review the new results from AUGER and LHC experiments.
Recent theoretical developments in the studies of two-photon exchange effects in elastic electron-proton scattering are reviewed. Two-photon exchange mechanism is considered a likely source of discrepancy between polarized and unpolarized experimental measurements of the proton electric form factor at momentum transfers of several GeV$^2$. This mechanism predicts measurable effects that are currently studied experimentally.
