Julia Guttmann, Nikolai Kivel, Mehdi Meziane, Marc Vanderhaeghen
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.
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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…
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 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…
Lévy $α$-stable generalization of the ReBB model of elastic proton-proton and proton-antiproton scattering
本文将ReBB模型推广到Lévy α-稳定情形，用于描述弹性质子-质子和质子-反质子散射，并探讨了其未来拟合实验数据的潜力。
Talk presented by S.M. Bilenky at the Adriatico Research Conference on "Trends in Collider Spin Physics", ICTP, Trieste, December 1995.
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 $Q^2$.
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…
A QCD interpretation of the scaling observed in the LHC proton-proton elastic cross-sections at moderate transfer momentum
本文用QCD饱和框架解释LHC质子-质子弹性散射在中等转移动量下的标度现象，指出硬振幅经幺正化构成pp振幅，且标度指数支持饱和标度指数约为硬过程二分之一的QCD饱和方法。
A new method for the determination of the real part of the elastic scattering amplitude is examined for high energy proton-proton and proton-nuclei elastic scattering at small momentum transfer. This method allows to decrease the number of model assumptions, to obtain the real part in the narrow region of momentum transfer and to test different models for hadron-nuclei scattering.
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.
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…
Odderon Exchange in Elastic Proton-Proton and Proton-Antiproton Scattering at TeV Energies
本论文详述了通过分析LHC和Tevatron在TeV尺度下的弹性散射测量数据，最终在强相互作用的非微扰域中发现了48年来悬而未决的Odderon交换。
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.
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.
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…
Several methods of extracting the magnitude of the real parts of the elastic hadron scattering amplitude - from the experimental data are presented. These methods allows us to obtain the real parts at one definite point of the transfer momentum and with a high accuracy without knowledge of the precise values of the normalization coefficient and with minimum theoretical assumptions.
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…
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.
Scaling of the elastic proton-proton cross-section
本文研究弹性质子-质子截面的标度性质，发现微分截面凸起与凹陷位置之比在宽能量范围内恒定，并由此推导出ISR的几何标度和LHC的新标度律。
The diffraction slope parameter is investigated for elastic proton-proton and proton-antiproton scattering based on the all available experimental data at low and intermediate momentum transfer values. Energy dependence of the elastic diffraction slopes is approximated by various analytic functions. The expanded "standard" logarithmic approximations with minimum number of free parameters allow to describe experimental slopes in all available energy range reasonably. The estimations of asymptotic shrinkage parameter $α'_{\cal{P}}$ were obtained for various $|t|$ domains based on the all availab…
We calculate the leading twist contribution to near-forward proton-proton (and proton-antiproton) elastic scattering with large momentum transfer, in the multiple scattering (Landshoff) mechanism. The amplitude in the near-forward region is dominated by singlet exchange for all three valence quark-quark scatterings. We assume the existence of a hard singlet quark-quark amplitude, which we estimate to be ${\cal O}(α_s^2/t)$. For a three-quark state whose transverse size is less than $1/Λ_{\rm QCD}$, Sudakov resummation accounts for both approximate $\d σ^{pp}/ \d t \sim t^{-8}$ at moderate $t$,…
The HJET Polarized Atomic Hydrogen Gas Jet Target polarimeter (HJET) polarimeter was designed to measure the absolute polarization of the proton beams at the Relativistic Heavy Ion Collider. In these measurements, the small scattering angle elastic $pp$ single $A_N(t)$ and double $A_{NN}(t)$ spin analyzing powers can be precisely determined. The experimental accuracy achieved at HJET requires corrections to the $A_N(t)$ parametrization, conventionally used for such studies. In this paper we evaluate the corrections to the analyzing powers due to (i) the differences between the electromagnetic …
A statistical analysis of the elastic unpolarized electron proton scattering data shows that, at large momentum transfer, the size and the $ε$ dependence of the radiative corrections, as traditionally calculated and applied, may induce large correlations of the parameters of the Rosenbluth fit, which prevent a correct extraction of the electric proton form factor. Using the electron QED structure (radiation) function approach the cross section of elastic electron-proton scattering in leading and next-to leading approximations is calculated and expressed as a correction to the Born cross sectio…
Lepton mass effects play a decisive role in description of elastic lepton-proton scattering when the beam's energy is comparable to the mass of the lepton. The future MUSE experiment, which is devised to solve the "Proton Radius Puzzle", is going to cover the corresponding kinematic region for a scattering of muons by a proton target. We anticipate that helicity-flip meson exchanges will make a difference in comparison of elastic electron-proton versus muon-proton scattering in MUSE. In this article, we estimate the $σ$ meson exchange contribution in the $t$-channel. This contribution, mediate…
The recently developed Lévy imaging method enables to extract an important physics information on hadron structure at high energies and ultra-low momentum transfers directly from elastic scattering data. In this work, we employ such a model-independent method to probe the internal structure of the proton and quantify its inelasticity profile in the impact parameter space emerging in proton-proton collisions at the highest available energy of $\sqrt{s} = 13$ TeV. The inelasticity profile function and its error band for the proton and its substructure have been reconstructed at different energie…
We investigate the effect of high order radiative corrections in unpolarized electron proton elastic scattering and compare with the calculations at lowest order, which are usually applied to experimental data. We show that higher order terms play a role, starting from values of the momentum transfer squared, $Q^2$, larger than the electron mass. Particular attention is devoted to the $ε$ dependence of radiative corrections.
We estimate the two-photon exchange contribution to elastic electron-proton scattering at large momentum transfer through the scattering off a parton in the proton. We relate the process on the nucleon to the generalized parton distributions which also enter in other wide angle scattering processes. We find that when taking the polarization transfer determinations of the form factors as input, adding in the 2 photon correction, does reproduce the Rosenbluth data.
Model independent radiative correction to the recoil proton polarization for the elastic electron-proton scattering is calculated within method of electron structure functions. The explicit expressions for the recoil proton polarization are represented as a contraction of the electron structure and the hard part of the polarization dependent contribution into cross-section. The calculation of the hard part with first order radiative correction is performed. The obtained representation includes the leading radiative corrections in all orders of perturbation theory and the main part of the secon…
A new version of Monte Carlo generator ELRADGEN for simulation of real photon emission in elastic electron-proton scattering is presented. The extensions in the new version include opportunity to deal with polarized particles: longitudinally polarized electron and arbitrary polarized proton. Simulation strategy, specifications of used kinematics, structure of the contributions to the observed cross section, cross-checks, and numerical results for BLAST experimental setup are presented and briefly discussed.
We estimate the two-photon exchange contribution to elastic electron-proton scattering at large momentum transfer $Q^2$. It is shown that the leading two-photon exchange amplitude behaves as $1/Q^4$ relative to the one-photon amplitude, and can be expressed in a model independent way in terms of the leading twist nucleon distribution amplitudes. Using several models for the nucleon distribution amplitudes, we provide estimates for existing data and for ongoing experiments.
We reanalyze the most recent data on elastic electron proton scattering. We look for a deviation from linearity of the Rosenbluth fit to the differential cross section, which would be the signature of the presence of two photon exchange. The two photon contribution is parametrized by a one parameter formula, based on symmetry arguments. The present data do not show evidence for such deviation.
We show that measurements of the proton's polarization in electron-positron annihilation to a proton-antiproton pair $e^+ e^- \to p \bar p$ strongly discriminate between the analytic forms of models which fit the proton form factors in the spacelike region. In particular, the single-spin asymmetry normal to the scattering plane measures the relative phase difference between the timelike $G_E$ and $G_M$ form factors. The expected proton polarization in the timelike region is large, of order of several tens of percent.
The spin correlation parameters, polarization - $A_{N}$ and double spin correlation parameters - $A_{NN}$, are calculated in the framework of dynamical model (GKS) of the hadron-hadron interection in the whole region of small angles and for energy HERA-N $\sqrt{s}=40 GeV$. It is shown that the measurements of such spin effects at small trunsfer momenta, in the region of the dip structure and at $t=-4 GeV^{2}$ have to give significant values of such spin correlation parameters.
We estimate the beam-normal single-spin asymmetry in elastic lepton-proton scattering without employing the ultrarelativistic approximation. Our calculation is relevant for analyses of muon scattering at energies of few hundred MeV and below -- when effects of the muon mass become essential. At such energies, the transverse polarization of the muon beam is expected to contribute significantly to the systematic uncertainty of precision measurements of elastic muon-proton scattering. We evaluate such systematics using an example of the MUSE experiment at PSI. The muon asymmetry is estimated at a…
Dark photon emission in elastic proton bremsstrahlung
本研究考虑质子间非零动量传递，修正弹性质子轫致辐射中0.4-1.5GeV暗光子的产生截面计算，结果与广义魏茨泽克-威廉姆斯近似吻合，却显著异于广泛使用的Blumlein和Brunner结果。
Scaling laws of elastic proton-proton scattering differential cross sections
本文揭示了弹性质子-质子散射微分截面在ISR到LHC能区具有普适的凸起-低谷位置比值常数，据此比较了不同标度律，并论证了LHC存在一族标度律及其对散射振幅参数化的约束。
The influence of the hard photon emission on the charge asymmetry in the (anti)lepton-proton elastic scattering was evaluated for the first time beyond the ultrarelativistic limit, while retaining the lepton mass at all steps of the calculation. This contribution - responsible for the charge asymmetry - is induced by interference between real photon emission from the lepton and proton. During the calculation any excited states of the intermediated proton are not considered, allowing us to use the standard fermionic propagator for this particle. The infrared divergence extracted using Lorenz-in…
We apply a "color" tripole ansatz for describing the $D$-term of the proton. By fitting the experimental data of the vector meson J/$ψ$ and $ϕ$ photoproductions near the thresholds, we firstly obtained the gluonic $D$-term of the proton. $D_g(0)$ is estimated to be $-2.16\pm0.42$ for J/$ψ$ and $-1.31\pm0.48$ for $ϕ$, and the mechanical root mean square radius of proton is estimated to be $0.61\pm0.29$ fm for $ϕ$ and $0.42\pm0.11$ fm for J/$ψ$.
We investigate the effect of high order radiative corrections in unpolarized electron proton elastic scattering and compare with the calculations at lowest order, which are usually applied to experimental data. Particular attention is devoted to the $ε$ dependence of radiative corrections, which is directly related to the electric proton form factor. We consider in particular the effects of the interference terms for soft and hard photon emission. Both quadratic amplitude describing the collinear emission along the scattered electron as well as the interference with the amplitudes of emission …
We examine a suggestion to use ${p-} ^4{He}$ elastic scattering, as an absolute polarimeter for high-energy polarized proton beams, by means of a Coulomb-Nuclear Interference effect for the single-spin asymmetry $A_N(t)$, around the diffractive minimum of the differential cross section $|t|\sim 0.21 GeV^2$. Although this reaction has a fairly simple dynamical structure, our theoretical uncertainties and the present experimental inaccuracy of the differential cross section in this $t$ region, allows one to generate dramatic effects for $A_N(t)$, which will be discussed.
We estimate the contribution of nonperturbative quark-gluon chromomagnetic interaction to the high energy elastic proton-proton cross section at large momentum transfer. It is shown that this contribution is very large in the accessible kinematic region of the present experiments. We argue that Odderon which is the $P=C=-1$ partner of Pomeron, is governed by the spin-flip component related to the nonperturbative three-gluon exchange induced by the anomalous quark chromomagnetic moment. We discuss the possible spin effects in the elastic proton-proton and proton-antiproton scattering coming fro…
The parity-conserving single-spin beam asymmetry of elastic electron-proton scattering is induced by an absorptive part of the two-photon exchange amplitude. We demonstrate that this asymmetry has logarithmic and double-logarithmic enhancement due to contributions of hard collinear quasi-real photons. An optical theorem is used to evaluate the asymmetry in terms of the total photoproduction cross section on the proton, predicting its magnitude at a few parts per million for high electon beam energies and small scattering angles. At fixed 4-momentum transfers, the asymmetry is rising logarithmi…
Towards an integrated determination of proton, deuteron and nuclear PDFs
本文通过整合nNNPDF3.0与NNPDF4.0拟合框架，推进质子、氘核及直至铅核的PDFs一体化测定，为非微扰QCD全局分析及EIC等设施研究奠定基础。
An extraction of the longitudinal proton structure function FL(x,Q2) from H1 data at low Q2 (about 1 GeV2) and low Bjorken x (about 0.00005) is reported. The analysis is based on the data collected in a dedicated low Q2 running period in 1999 and during shifted vertex runs in 2000. Two methods of extracting FL(x,Q2) are discussed and shown to give consistent results. Theoretical predictions are compared with the data.
The validity of some rules in the classical theory of spin, which are followed by the Bargmann--Michel--Telegdi formula for a relativistic particle spin rotation in a constant homogeneous magnetic field, is analyzed. In the framework of the quantum theory, we give examples where these rules are violated. Consequences for polarization experiments are discussed.
Analytical Evaluation of Elastic Lepton-Proton Two-Photon Exchange in Chiral Perturbation Theory
本文在重子手征微扰理论框架下，以次领头阶精度解析计算了弹性轻子-质子散射中的双光子交换贡献，识别了软光子近似缺失项，并分析了缪子与电子散射的差异。
The Bialas-Bzdak model of elastic proton-proton scattering is generalized to the case when the real part of the parton-parton level forward scattering amplitude is non-vanishing. Such a generalization enables the model to describe well the dip region of the differential cross-section of elastic scattering at the ISR energies, and improves significantly the ability of the model to describe also the recent TOTEM data at sqrt{s} = 7 TeV LHC energy. Within this framework, both the increase of the total cross-section, as well as the decrease of the location of the dip with increasing colliding ener…
Using a recent next-to-leading-order calculation of the photoproduction double differential cross section for heavy quarks, we study the possibility of extracting the gluon density of the proton from heavy-quark photoproduction data. We discuss the theoretical uncertainties connected with this method, and we conclude that they are well under control in a wide $x$ domain.
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