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 elastic and inelastic profiles have been derived from the measured elastic differential cross section data with the help of exact impact parameter representation of elastic scattering amplitude. The results obtained for $pp$ scattering at energy of 53 GeV and $\bar{p} p$ scattering at energy of 541 GeV have been presented. They indicate that nucleons can be regarded as objects characterized by a small core (diameter $\sim$ 0.4$÷$0.8 fm) and a half transparent outer shell (responsible mainly for elastic hadron scattering).
Total and differential cross sections for high energy and small momentum transfer elastic hadron-hadron scattering are studied in QCD using a functional integral approach. The hadronic amplitudes are governed by vacuum expectation values of lightlike Wegner-Wilson loops, for which a matrix cumulant expansion is derived. The cumulants are evaluated within the framework of the Minkowskian version of the model of the stochastic vacuum. Using the second cumulant, we calculate elastic differential cross sections for hadron-hadron scattering. The agreement with experimental data is good.
This report discusses some results on differential cross sections for high energy and small momentum transfer elastic hadron-hadron scattering in QCD, using a functional integral approach. In particulary a matrix cumulant expansion for the vacuum expectation values of lightlike Wegner-Wilson loops, which governs the hadronic amplitudes, is presented. The cumulants are evaluated using the model of the stochastic vacuum.
With relation to the RHIC spin program we research the polarization effects in elastic proton-proton scattering at small momentum transfer and in the diffraction dip region. The calculations take into account the Coulomb-hadron interference effects including the additional Coulomb-hadron phase. In particular we show the impact of the form of the hadron potential at large distances on the behavior of the hadron spin-flip amplitude at small angles. The $t$-dependence of the spin-flip amplitude of high energy hadron elastic scattering is analyzed under different assumptions on the hadron interact…
In this paper we prove a new optimal bound on the logarithmic slope of the elastic slope when: elastic cross section and differential cross sections in forward and backward directions are known from experimental data. The results on the experimental tests of this new optimal bound are presented in Sect. 3 for the principal meson-nucleon elastic scatterings: pion-nucleon, kaon-nucleon at all available energies. Then we have shown that the saturation of this optimal bound is observed with high accuracy practically at all available energies in meson-nucleon scattering.
The commonly used West and Yennie integral formula for the relative phase between the Coulomb and elastic hadronic amplitudes might be consistently applied to only if the hadronic amplitude had the constant ratio of the real to the imaginary parts al all kinematically allowed values of four momentum transfer squared.
In this work the process of elastic hadron scattering is discussed. In particular, scattering amplitudes for the various Pomeron models are compared. In addition, differential elastic cross section as a function of the scattered proton transverse momentum for unpolarised and polarised protons is presented. Finally, an implementation of the elastic scattering amplitudes into the GenEx Monte Carlo generator is discussed.
We update the comparison with experiment of the dynamical model of high-energy hadron interactions based on the two scale structure of hadrons. All predictions made over decade ago are confirmed with a high precision by the TOTEM experiment at LHC.
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.
The commonly used West and Yennie model approach to the description of the interference between Coulomb and hadronic scattering of nucleons is critically examined and its deficiencies are clarified. The preference of the more general eikonal model approach is summarized.
We consider a multi-channel correction accounting for intermediate transitions inside an equivalence class of diffractive states. Our formalism of 'diffractive limit' provides an excellent description of elastic and inclusive inelastic scattering of high energy (53 - 546 GeV) protons and antiprotons.
Non-forward elastic hadron-scattering data are collected and analysed within the Regge approach. Through an analysis of the data in small bins in $t$, we have directly extracted the pomeron trajectory and the hadronic form factors (or reggeon couplings). We found higher values than usually used for the intercept and for the slope of the soft pomeron trajectory. The presence of zeros in $t$ for the effective hadronic form factors is emphasised.
The different models of elastic nucleon scattering amplitude will be discussed. Especially, the preference of the more general approach based on eikonal model will be summarized in comparison with the West and Yennie amplitude that played an important role in analyzing corresponding experimental data in the past.
We review the main results we have obtained in the area of high-energy elastic hadron scattering and presented in this series of Workshops on Hadronic Interactions. After an introduction to some basic experimental and theoretical concepts, we survey the results reached by means of four approaches: analytic models, model-independent analyses, eikonal models and nonperturbative QCD. Some of the ongoing researches and future perspectives are also outlined.
Compact analytical formulae for QED radiative corrections in the processes of elastic $e-p$ scattering are obtained in the case when kinematic variables are reconstructed from the recoil proton momentum measured. Numerical analysis is presented under kinematic conditions of current experiments at JLab.
A brief review on the Dipole Pomeron model is given. The model not only describes data on hadron-hadron interactions, but also allows to describe data on the proton structure function with a $Q^2$ independent intercept. Moreover the chosen Dipole Pomeron has an intercept equal to one and does not violate unitarity limit on the total elastic cross-section.
The new parameterization of the Generalized Parton Distributions (GPDs) t-dependence is investigated. It is shown that the new form of the GPDS allows one to reproduce sufficiently well the electromagnetic form factors of the proton and neutron at small and large momentum transfer and obtain a good description of the elastic nucleon-nucleon scattering at high energies.
Under the assumption of total absorption and dominance of the imaginary part of the scattering amplitude, we present a sum rule for any hadronic elastic differential cross-section ${dσ}\over{dt}$: the dimensionless quantity ${{1}\over{2}}\int (dt)\sqrt{{{1}\over π}{{dσ}\over{dt}}} \to 1$, at asymptotic energies. Experimental data from ISR and Tevatron confirm a trend towards its saturation and some estimates are presented for LHC. Its universality and further consequences for the nature of absorption in QCD based models for elastic and total cross-sections are explored.
The rôle of inelastic diffraction in elastic scattering of nuclei is studied in the formalism of \emph{diffractive limit}. The results obtained for scattering of the $α$--particles on light nuclei show that the nucleonic diffraction is especially important at large momentum transfers where the Glauber model of geometric diffraction fails.
A numerical analysis of QED radiative corrections for elastic e(mu)p cattering in hadronic variables at energies of the current experiment at JLab is performed. The explicit formulas from the review of Akhundov et al. resulting from the integration over the phase space of leptonic variables plus photon are used to obtain the values of the cross sections and the radiative correction factor for unpolarized lepton-proton scattering. Our numerical results agree with the corresponding results arising from the formulas of Afanasev et al.
We analyse the 13 TeV TOTEM data on elastic proton-proton scattering through a thorough statistical analysis, and obtain that $ρ=0.096\pm 0.006$ and $σ_{tot}=(107.5\pm 1.5)$ mb. Theoretical errors could lower the cross section by about 2 mb and increase $ρ$ by about 0.002. We also show that these results do not imply the existence of an odderon at $t=0$.
We have confirmed and complemented previous conclusions from studies of the impact parameter profiles, relative to $pp$ and $\bar pp$ scattering, using a generalized eikonalized amplitude. In particular, the transition from the grey to the black disk is followed, when the energy increases beyond $\sim 3$ TeV and for the inelastic process, by a black ring surrounding the antishadow scattering mode at the center. The ranges of hadronic forces responsible for the elastic and inelastic processes are estimated by means of root-mean-squares of the impact parameter. Predictions at the LHC energy are …
In the framework of the model, where the scattering amplitude is determined by the first and second moments of the GPDs, the qualitative description of all existing experimental data at $\sqrt{s} \geq 52.8 $ GeV, including the Coulomb range and large momentum transfers, is obtained with only 4 free parameters. The spin-flip amplitude of the nucleon-nucleon elastic scattering is determined taking into account the spin-dependence part of the second moment of the generalized parton distributions (GPDs) with a new set of $t $-dependence. The corresponding value of the % analyzing power $A_N$ for t…
First, I define generalized Bloom-Gilman duality and Bjorken-like scaling for inclusive photoproduction of pions, relating Quark-Parton Model description in the deep-inelastic region to the properties of exclusive resonance excitation. Secondly, connection between inclusive and exclusive processes is established in the formalism of Nonforward Parton Densities used here to predict deviations from dimensional scaling for a variety of observables: nucleon and pion elastic form factors, and pion Compton scattering.
Starting from a short range expansion of the inelastic overlap function, capable of describing quite well the elastic pp and $\bar{p}p$ scattering data, we obtain extensions to the inelastic channel, through unitarity and an impact parameter approach. Based on geometrical arguments we infer some characteristics of the elementary hadronic process and this allows an excellent description of the inclusive multiplicity distributions in $pp$ and $\bar{p}p$ collisions. With this approach we quantitatively correlate the violations of both geometrical and KNO scaling in an analytical way. The physical…
The scattering amplitude in the dual model with Mandelstam analyticity and trajectory $α(s)=α_{0}-γ\ln [ (1+β\sqrt{s_{0} -s})/(1+ β\sqrt{s_{0}})]$ is studied in the limit $s,|t|\to \infty, s/t=const.$ By using the saddle point method, a series decomposition for the scattering amplitude is obtained, with the leading and two sub-leading terms calculated explicitly.
A behavior of imaginary and real parts of the high-energy elastic hadron scattering amplitude is examined in the diffraction region. It is shown that the interference between Coulomb and hadronic scattering at small momentum transfers and especially in the region of diffractive minimum can bring some information about the structure of the hadron spin-non-flip amplitude.
In the present review we discuss different aspects of the two-photon exchange (TPE) physics in elastic $ep$ scattering, at high $Q^2$ as well as at low $Q^2$. The imaginary part of the TPE amplitude gives rise to beam and target single-spin asymmetries. Different theoretical approaches to calculation of these observables are considered. The real part of the TPE amplitude influence unpolarized cross section and double-spin observables and is, most likely, responsible for discrepancy between two methods of proton form factors measurements. We review different methods of calculations of the TPE a…
The spin effects in the elastic proton-proton scattering are analysed at NICA energies. It is shown the importance the investigation of the region of the diffraction minimum in the differential cross sections. Some possible estimation of spin effects are given for the different NICA energies in the framework of the new high energy generelazed structure (HEGS) model.
The elastic scattering of gqq, gqqbar and gqbarqbar and the thermalization of quark-gluon matter are studied. According to Feynman diagrams at the tree level, squared amplitudes for the elastic gqq scattering and the elastic gqqbar scattering are derived in perturbative QCD. Transport equations including the squared amplitudes for the elastic gqq, gqqbar and gqbarqbar scattering are established. Corresponding to anisotropic gluon and quark distributions created in central Au-Au collisions at RHIC, solutions of the transport equations show that thermalization time of quark matter can be shorten…
A new method for the determination of the real part of the elastic scattering amplitude is examined for high energy proton-proton elastic scattering at small momentum transfer. This method allows us to decrease the number of model assumptions, to obtain the real part in a narrow region of momentum transfer and to test different models. The real part is computed at a given point t_min near t=0 from the known Coulomb amplitude. Hence one obtains an important constraint on the real part of the forward scattering amplitude and therefore on the rho-parameter (measuring the ratio of the real to imag…
In this paper we applicate eikonalization procedure to the processes of elastic scattering at high energies. We have shown, that elastic data is consistent with relatively low values of eikonal parameter $c_p < 1$ only. It is in contrast with theoretical considerations.
Deep--elastic scattering and its role in discrimination of the possible absorptive and reflective asymptotic scattering mechanisms are discussed with emphasis on the difference in the experimental signatures related to production processes.
We discuss how the reflective scattering would affect elastic scattering in the region of small and moderate values of $-t$, in particular, we demonstrate that diffractive pattern in the angular distribution will be kept in a modified form.
The theory of the perturbative pomeron, due to Lipatov and collaborators, is used to compute the probability of observing parton-parton elastic scattering and rapidity gaps between jets in hadron collisions at Tevatron energies.
A model for elastic scattering of nucleons (and anti-nucleons) based on the quark-diquark representation of the nucleon with springy Pomeron, providing increased real part of the scattering amplitude, is developed. The model predictions are compared with experimental data for the differential elastic cross-sections of nucleons in the energy range from few GeV up to 7 TeV using available databases.
The theory of the perturbative pomeron, due to Lipatov and collaborators, is used to compute the probability of observing parton-parton elastic scattering and rapidity gaps between jets in hadron collisions at SSC and LHC energies.
This is a short review of the physics of single-spin asymmetries caused by two-photon exchange in elastic scattering of electrons by nucleons and nuclei.
Summary of the XIth International Conference on Elastic and Diffractive Scattering in Chateau de Blois, France, May 15 - 20, 2005, summarizing both theoretical and experimental presentations and discussions.
We asses a role of the double helicity-flip amplitudes in small-angle elastic pp-scattering and obtain a new unitary bound for the double helicity-flip amplitude F_2 in elastic pp-scattering at small values of t on the basis of the U-matrix method of the s-channel unitarization.
The problems linked to the extraction of the basic parameters of the hadron elastic scattering amplitude at the LHC are explored. The impact of the Black Disk Limit (BDL)$-$ which constitutes a new regime of the scattering processes - on the determination of these values is examined.
Dominant contributions of enhanced Pomeron diagrams to elastic hadron-hadron scattering amplitude are re-summed to all orders. The formalism is applied to calculate total hadronic cross sections and elastic scattering slopes. An agreement with earlier results is obtained.
Scenario for restoration of the real part of the elastic scattering amplitude has been proposed for the unitarity saturation case. Dependence of the real part of the elastic scattering amplitude on the transferred momentum $-t$ at the asymptotical energies has been restored from the corresponding imaginary part on the basis of derivative analyticity relations (analytization procedure).
Predictions of the elastic proton-proton cross sections at energies of LHC are calculate on the base of the high energy dynamical model. The growth of $ds/dt$ at fixed transfer momenta are shown. The form of eikonal of elastic hadron scattering at super high energies is discussed.
The theory of the perturbative pomeron, due to Lipatov and collaborators, is used to compute the probability of observing parton-parton elastic scattering and rapidity gaps between jets in hadron collisions at very high energies.
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.
We comment on the papers "Nucleon elastic form factors and local duality" [Phys. Rev. {\bf D62}, 073008 (2000)] and "Experimental verification of quark-hadron duality" [Phys. Rev. Lett. {\bf 85}, 1186 (2000)]. Our main comment is that the reconstruction of the proton magnetic form factor, claimed to be obtained from the inelastic scaling curve thanks to parton-hadron local duality, is affected by an artifact.
High energy $pp$ and $p\bar p$ elastic scattering is treated in the framework of Additive Quark Model. The reasonable agreement with experimental data is achieved with the natural parameters for the strong matter distribution inside proton.
When colliding, the high energy hadrons can either produce new particles or scatter elastically without change of their quantum numbers and other particles produced. Namely elastic scatterings of hadrons are considered in this paper. The general machinery of their theoretical treatment is described. Some new experimental data are presented and confronted to phenomenological approaches. The internal structure of hadrons is the main subject of these studies. Its impact on properties of their interactions is reviewed. It is shown that protons become larger and darker with increase of their collis…
I discuss recent progress in the theory of exclusive meson production and Compton scattering, focusing on hard-scattering factorization and on the dipole formalism.
A method of 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. The method allows to decrease the number of model assumptions, to obtain the real parts of the spin non-flip and spin-flip amplitudes in the narrow region of momentum transfer.
We calculate two-photon exchange amplitude for the elastic electron-pion scattering in the dispersion-relation inspired approach, including both elastic and inelastic contributions. The latter was modelled as a sum of ρand b_1(1235) meson contributions. We find that at Q^2 < 2 GeV^2 the elastic contribution is dominant, similarly to electron-proton scattering case. At higher Q^2 the inelastic contribution is not negligible, but still smaller than the elastic one. We also explain observed rapid amplitude growth at backward angles.
