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 interpreted well as the superposition of mutual collisions of two internal structures with maximal external dimensions; the approximate dimensions and frequencies of corresponding structures being established on the basis of measured elastic data.
The main contribution to hard elastic scattering comes from components of wave functions of colliding hadrons that contain minimum number of partons. We discuss this mechanism in regge and parton approaches and estimate the probabilities that colliding hadrons are in such bare states. The behavior of cross-sections in this regime at various energies can give nontrivial information on high energy dynamics.
The next-to-leading order of the differential cross-section of the subprocess of Compton scattering of quark-gluon of prompt photon production in proton-proton collisions at NICA energies
Baku State University（巴库国立大学）；Institute for Physical Problems, Baku State University（巴库国立大学物理问题研究所）
The influence of the electron spin degree of freedom on nonperturbative electron-positron pair production by high-energy proton impact on an intense laser field of circular polarization is analyzed. Predictions from the Dirac and Klein-Gordon theories are compared and a spin-resolved calculation is performed. We show that the various spin configurations possess very different production probabilities and discuss the transfer of helicity in this highly nonlinear process. Our predictions could be tested by combining the few-TeV proton beam at CERN-LHC with an intense laser pulse from a table-top…
The next-to-leading order of the differential cross section of the subprocess of annihilation of quark-antiquark pair of prompt photon production in proton-proton collisions at NICA energies
Baku State University（巴库国立大学）；Institute for Physical Problems, Baku State University（巴库国立大学物理问题研究所）
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…
We recall the main properties of inclusive particle distributions expected for Pomeron-proton and Pomeron-Pomeron interactions. Due to the small size of the Pomeron we expect larger transverse momenta of secondaries and a smaller probability of Multiple Interactions, that is a narrower multiplicity distribution. We propose to compare the spectra of secondaries produced in the Pomeron and the proton interactions in terms of the Feynman $x_F$ variable. The main difference should be observed for a relatively large $x_F$, that is near the edge of rapidity gaps. Such data offer the opportunity to i…
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…
We present the potential to determine the polarised gluon density from boson-gluon fusion processes with di-jet events at future high energy ep-colliders. These include HERA at DESY operated with polarised electrons and protons, polarised protons from HERA colliding on polarised electrons from a future linear collider, and polarised protons from RHIC at BNL colliding on electrons from a future electron accelerator.
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.
We present a formalism for gluon-gluon elastic scattering in the presence of the classical color field of the protons in high energy collision. The classical field is obtained by solving the classical Yang-Mills equation in the covariant gauge and treated as a prescribed background for the quantum gluons involved in the scattering process. The interaction between the classical field and the quantum gluon modifies the gluon propagator, and, in turn, the $gg\rightarrow gg$ amplitude. The modified gluon propagator is derived to the first non-zero order of the classical field using the Gaussian ap…
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…
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…
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.
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.
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…
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.
Fermi Gamma ray Space Telescope measurements of spectra, variability time scale, and maximum photon energy give lower limits to the apparent jet powers and, through gammagamma opacity arguments, the bulk Lorentz factors of relativistic jets. The maximum cosmic-ray particle energy is limited by these two quantities in Fermi acceleration scenarios. Recent data are used to constrain the maximum energies of cosmic-ray protons and Fe nuclei accelerated in colliding shells of GRBs and blazars. The Fermi results indicate that Fe rather than protons are more likely to be accelerated to ultra-high ener…
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.
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…
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…
An important experiment for cosmic ray physics is going to be conducted with the colliding proton beams of the CERN LHC. The equivalent energy of the 14 TeV center of mass energy of the colliding proton beams in the LHC is 1017eV in the laboratory frame. Two small electromagnetic calorimeters have been installed at zero degree collision angle +/-140m from the interaction point IP1. The calorimeters measure the energies and the positions of the axes of showers produced by forward neutral particles created in the proton-proton collisions. The shower calorimeters are therefore able to measure the…
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 …
I present an overview of the ridge phenomenon in proton-proton and proton-lead collisions. This novel collimation between rapidity separated hadron pairs is a consequence of non-linear gluon dynamics within the small-x wave-function of the colliding hadrons.
Using numerical holography, we study the collision of a planar sheet of energy with a bounded localized distribution of energy. The collision, which mimics proton-nucleus collisions, produces a localized lump of debris with transverse size $R \sim 1/T_{\rm eff}$ with $T_{\rm eff}$ the effective temperature, and has large gradients and large transverse flow. Nevertheless, the postcollision evolution is well described by viscous hydrodynamics. Our results bolster the notion that debris produced in proton-nucleus collisions may be modeled using hydrodynamics.
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.
