Standard parton distribution functions contain neither information on the correlations between partons nor on their transverse motion, then a vital knowledge about the three dimensional structure of the nucleon is lost. Hard exclusive processes, in particular DVCS, are essential reactions to go beyond this standard picture. In the following, we examine the most recent data in view of the dipole model predictions and their implication on the quarks/gluons imaging (tomography) of the nucleon.
We give an overview of jet physics in deeply inelastic scattering at HERA. The problem of jet definitions, the scale dependence of jet cross sections and some applications are discussed. (Talk presented at the Workshop on Deeply Inelastic Scattering and QCD, Paris, April 1995. To appear in the proceedings.)
Exclusive vector meson production and deeply virtual Compton scattering are ideally suited reactions for studying the structure of the proton and the transition from soft to hard processes. The main experimental data obtained at HERA are summarised and presented in the light of QCD approaches.
We demonstrate that the measurement of an azimuthal angle asymmetry in deeply virtual Compton scattering (DVCS) at HERA energies, is experimentally feasible and allows one to determine for the first time the ratio $η$, of the real to imaginary part of the DIS amplitude. We further show that such a measurement would discriminate between different scenarios of the energy dependence of $F_2(x,Q^2)$ at energies beyond those reachable at HERA.
A next-to-leading order Monte Carlo program for the calculation of heavy quark cross sections in deeply inelastic scattering is described. Concentrating on charm quark and D^*(2010) production at HERA, several distributions are presented and their variation with respect to charm quark mass, parton distribution set, and renormalization-factorization scale is studied.
A new measurement is presented of elastic deeply virtual Compton scattering (DVCS) based on data taken by the H1 detector during the complete HERA II period. The data are well described by QCD based calculations. For the first time, a beam charge asymmetry is obtained in a colliding mode, using data recorded in $e^-p$ and $e^+p$. A significant non zero value is measured, related to the interference of QCD and QED processes, namely the DVCS and Bethe-Heitler reactions.
We compare recent experimental results for one-particle-inclusive processes in deeply inelastic scattering at HERA with theoretical predictions in next-to-leading-order QCD perturbation theory, and study the factorization scale dependence of cross sections and charged multiplicities. In the future, for the HERA machine running at design luminosity, scaling violations of fragmentation functions permit the measurement of the strong coupling constant. We estimate the size of the statistical error of $α_s$ that can be achieved, and study the theoretical error due to the various parton density para…
Deeply Virtual Compton Scattering (DVCS) in $ep$ collisions has emerged in recent years as a an essential reaction to obtain information on the correlation of partons in the hadron (proton) or on the transverse distribution of these partons. In these proceedings, we examine the lattest data from HERA (at low $x_{Bj}<10^{-2}$) and their impact on models. We analyse in detail what these data imply on the spatial structure of the proton. In particular, the most recent measurements of the Beam Charge Asymmetry by the H1 experiment is discussed in this context. Perspectives are presented for furthe…
Standard parton distribution functions contain neither information on the correlations between partons nor on their transverse motion, then a vital knowledge about the three dimensional structure of the nucleon is lost. Hard exclusive processes, in particular DVCS, are essential reactions to go beyond this standard picture. In the following, we examine the most recent data from HERA (at low $x_{Bj}<10^{-2}$) and their impact on GPD models. The most recent measurements of the Beam Charge Asymmetry by the H1 experiment is discussed. Perspectives are presented for further measurements of DVCS cro…
Standard parton distribution functions contain neither information on the correlations between partons nor on their transverse motion, then a vital knowledge about the three dimensional structure of the nucleon is lost. Hard exclusive processes, in particular DVCS, are essential reactions to go beyond this standard picture. In the following, we examine the most recent data and their implication on the quarks/gluons imaging (tomography) of the nucleon.
A Reggeometric (Regge+Geometry) model, based on the observed proportionality between the forward slope of the differential cross section and the interaction radius, the latter depending on virtuality Q2 of the incoming virtual photon and on the mass M 2 of the produced particle, is constructed. The objective of this study is the dependence of the Regge-pole amplitude on the virtuality Q2 and masses of the external particles, which remains an open problem for the theory. The present analysis is based on the HERA data on Deeply Virtual Compton Scattering (DVCS) and exclusive diffractive Vector M…
We present the first study of the QCD corrections to the color-singlet (CS) $J/ψ$ production in deeply inelastic $ep$ scattering at HERA. The $K$-factor ranges from $0.85$ to $2.38$ in the kinematic regions we study. In low transverse momentum regions, the $K$-factors is even smaller, and close to 1, which indicates good convergence of the perturbative expansion. With the QCD corrections, the CS cross section is still below the data. At least at QCD next-to-leading order, the color-octet mechanism is necessary to describe the data.
We present the recent experimental results from deeply virtual Compton scattering (DVCS) from H1 and ZEUS experiments at HERA. Their interpretation encoded in the generalized parton distributions is discussed.
Recent results from the HERA ep collider are discussed with emphasis on the transition from short to long distance phenomena in QCD. The results cover inclusive ep scattering, inclusive diffractive scattering, vector meson production, and deeply virtual Compton scattering (DVCS).
The recent results of the studies of Deeply Virtual Compton Scattering (DVCS) events at HERA are presented. The possibility offered by this process to gain information about skewed parton distributions (SPD) is emphasized.
A factorized Regge-pole model for deeply virtual Compton scattering is suggested. The use of an effective logarithmic Regge-Pomeron trajectory provides for the description of both ``soft'' (small $|t|$) and ``hard'' (large $|t|$) dynamics. The model contains explicitly the photoproduction and the DIS limits and fits the existing HERA data on deeply virtual Compton scattering.
Recent results obtained at HERA on deeply virtual Compton scattering and exclusive vector meson production are reviewed, with the emphasis on the transition from soft to hard diffraction and on spin dynamics.
It is established in the paper that experimental data on deeply virtual exclusive electroproduction of $ρ^0$- and $ϕ$-mesons may be described fairly well in the framework of a generalized Regge approach without additional, $Q^2$-dependent, singularities in the J-plane.
Deeply virtual meson production at HERA and at the EIC within the Color Glass Condensate EFT
CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院）；Dipartimento di Fisica, Università della Calabria（卡塔尼亚大学物理系）；INFN, Gruppo Collegato di Cosenza（意大利国家核物理研究所科森扎协作组）；National Centre for Nuclear Research (NCBJ)（波兰国家核研究中心）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎萨克雷大学）
Diffractive deeply inelastic scattering from a hadron is described in terms of diffractive quark and gluon distributions. If the transverse size of the hadronic state is sufficiently small, these distributions are calculable using perturbation theory. We present such a calculation and discuss the underlying dynamics. We comment on the relation between this dynamics and the pattern of scaling violation observed in the hard diffraction of large-size states at HERA.
We suggest a simple physical picture for the diffractive parton distributions that appear in diffractive deeply inelastic scattering. In this picture, partons impinging on the proton can have any transverse separation, but only when the separation is small can they penetrate the proton without breaking it up. By comparing the predictions from this picture with the diffractive data from HERA, we determine rough values for the small separations that dominate the diffraction process.
I report on an analysis of Deeply Virtual Compton Scattering (DVCS) within the dipole model, done in collaboration with M. McDermott and G. Shaw. The two models considered here are distinct in their structure and implications. They both agree with the available cross-section data on DVCS from HERA. Predictions for various asymmetries are also given.
Based on the two-gluon-exchange dynamical mechanism for deeply inelastic scattering at low x ~= Q^2/W^2 <<1, we stress the intimate connection between the total virtual photoabsorption cross section, deeply virtual Compton scattering and vector-meson electroproduction. A simple expression for the cross section for deeply virtual Compton scattering is derived. Parameter-free predictions are obtained for deeply-virtual Compton forward scattering and vector-meson forward production, once the parameters in the total virtual photoabsorption cross section are determined in a fit to the experimental …
The coefficient functions for heavy-flavour production in deeply inelastic electron-hadron scattering have been calculated previously. Analytic expressions are impossible to publish due to their length. Therefore we have tabulated them as two-dimensional arrays as is often done for the scale-dependent parton densities. Using this computer program we present event rates for charm production at HERA in bins of $x$ and $Q^2$. These rates are insensitive to variations in the factorization and renormalization scale $μ$.
Estimates for longitudinal spin asymmetries which single out new polarized nucleon structure functions in deeply inelastic charged current interactions at HERA energies are given, exploiting their interpretation in terms of polarized quark distributions. These asymmetries turn out to be large and allow a measurement of the new polarized structure functions $g_1^{W}$ and $g_5^{W}$, which would add valuable tests and information on the spin content of quarks inside a polarized proton. We also show that single spin asymmetries in neutral current interactions are very small.
We study deeply virtual Compton scattering (DVCS) on a deuteron target. We model the Generalized Quark Distributions in the deuteron by using the impulse approximation for the lowest Fock-space state. Numerical predictions are given for the unpolarized cross sections for the kinematical regimes relevant for JLab and HERMES at HERA. Differential cross sections show the same pattern as for the proton case and at low values of t they are of comparable size.
Measurement of the distribution of hadronic energy in the final state in deeply inelastic electron scattering at HERA can provide a good test of our understanding of perturbative QCD. For this purpose, we consider the energy distribution function, which can be computed without needing final state parton fragmentation functions. We compute this distribution function for finite transverse momentum q_T at order alpha_s, and use the results to sum the perturbation series to obtain a result valid for both large and small values of transverse momentum.
We study timelike and spacelike virtual Compton scattering in the generalized Bjorken scaling regime at next to leading order in the strong coupling constant, in the medium energy range which will be studied intensely at JLab12 and in the COMPASS-II experiment at CERN. We show that the Born amplitudes get sizeable O(α_s) corrections and, even at moderate energies, the gluonic contributions are by no means negligible. We stress that the timelike and spacelike cases are complementary and that their difference deserves much special attention.
Following recent predictions that the geometric scaling properties of deep inelastic scattering data in inclusive gamma*-p collisions are expected also in exclusive diffractive processes, we investigate the diffractive production of vector mesons. Using analytic results in the framework of the BK equation at non-zero momentum transfer, we extend to the non-forward amplitude a QCD-inspired forward saturation model including charm, following the theoretical predictions for the momentum transfer dependence of the saturation scale. We obtain a good fit to the available HERA data and make predictio…
We use gauge/gravity duality to study deeply virtual Compton scattering (DVCS) in the limit of high center of mass energy at fixed momentum transfer, corresponding to the limit of low Bjorken x, where the process is dominated by the exchange of the pomeron. Using conformal Regge theory we review the form of the amplitude for pomeron exchange, both at strong and weak 't Hooft coupling. At strong coupling, the pomeron is described as the graviton Regge trajectory in AdS space, with a hard wall to mimic confinement effects. This model agrees with HERA data in a large kinematical range. The behavi…
This is a talk given at Ringberg Workshop:"New Trends in HERA Physics", 30 May - 4 June, 1999.In this talk we discuss how deeply the region of high parton densities has been studied experimentally at HERA. We show that the measurements of deep inelastic structure functions at HERA confirm our theoretical expectation that at HERA we face a challenging problem of understanding a new system of partons: quarks and gluons at short distances with so large densities that we cannot treat this system perturbatively. We collect all experimental indications and manifestations of specific properties of hi…
A Pomeron model applicable to both "`soft" and "hard" processes is suggested and tested against the high-energy data from virtual photon-induced reactions. The Pomeron is universal, containing two terms, a "soft" and a "hard" one, whose relative weight varies with $\widetilde {Q^2}=Q^2+M_V^2$, where $Q^2$ is the virtuality of the incoming photon and $M_V$ is the mass of the produced vector particle. With a small number of adjustable parameters, the model fits all available data on vector meson production and deeply virtual Compton scattering from HERA. Furthermore, we attempt to apply the mode…
Recently the concept of the pion cloud in the nucleon turned out to be successful in understanding the Gottfried sum rule violation observed by the New Muon Collaboration and the Drell--Yan asymmetry measured in NA51 at CERN. We propose a further possibility to test this concept at HERA through the analysis of the structure of deep inelastic scattering (DIS) events induced by pion--exchange. Momentum and energy distributions of outgoing nucleons as well as rapidity and multiplicity distributions are investigated using Monte Carlo simulations. Most observables cannot distinguish this process fr…
We study radiative corrections to deeply virtual Compton scattering in the kinematics of HERA collider experiments to next--to--leading and next--to--next--to--leading order. In the latter case the radiative corrections are evaluated in a special scheme that allows us to employ the predictive power of conformal symmetry. As observed before, the size of next--to--leading order corrections strongly depends on the gluonic input, as gluons start to contribute at this order. Beyond next--to--leading order we find, in contrast, that the corrections for an input scale of few GeV^2 are small enough to…
Predictions for light charged hadron production data in the current fragmentation region of deeply inelastic scattering from the H1 and ZEUS experiments are calculated using perturbative Quantum Chromodynamics at next-to-leading order, and using fragmentation functions obtained by fitting to similar data from $e^+ e^-$ reactions. General good agreement is found when the magnitude $Q^2$ of the hard photon's virtuality is sufficiently large. The discrepancy at low $Q$ and small scaled momentum $x_p$ is reduced by incorporating mass effects of the detected hadron. By performing quark tagging, the…
We report on our recent calculation of the inclusive direct photo- and hadroproduction of the J/psi meson at next-to-leading order within the factorization formalism of nonrelativistic QCD. We fit the color-octet (CO) long-distance matrix elements <O^(J/psi)(1S0[8])>, <O^(J/psi)(3S1[8])> and <O^(J/psi)(3P0[8])> to the transverse momentum (p_T) distributions measured by CDF at Fermilab Tevatron and by H1 at DESY HERA and show that they also successfully describe the p_T distributions from PHENIX at BNL RHIC and CMS at the CERN LHC as well as the photon-proton c.m. energy and (with worse agreeme…
A very wide body of HERA diffractive electroproduction data is confronted with the predictions of the colour dipole model. In doing so we focus upon three different parameterisations of the dipole scattering cross-section, whose parameters are fixed by analysis of DIS structure function data. This analysis strongly suggests the presence of saturation effects, but is not definitive because the conclusion requires the inclusion of data at low-$Q^2$ values. Having fixed the parameters of the models from the DIS structure function data, the resulting dipole cross sections can be used to make genui…
Using the approach based on conformal symmetry we calculate the two-loop coefficient function for the axial-vector contributions to two-photon processes in the $\overline{\rm MS}$ scheme. This is the last missing element for the complete next-to-next-to-leading order (NNLO) calculation of the the pion transition form factor $γ^\astγ\to π$ in perturbative QCD. The corresponding high-statistics measurement is planned by the Belle II collaboration and will allow one to put strong constraints on the pion light-cone distribution amplitude. The calculated NNLO corrections prove to be rather large an…
We extend the multi-purpose Monte-Carlo event generator Sherpa to include processes in deeply inelastic lepton-nucleon scattering. Hadronic final states in this kinematical setting are characterised by the presence of multiple kinematical scales, which were up to now accounted for only by specific resummations in individual kinematical regions. Using an extension of the recently introduced method for merging truncated parton showers with higher-order tree-level matrix elements, it is possible to obtain predictions which are reliable in all kinematical limits. Different hadronic final states, d…
In this work, we investigate the exclusive production of particles in scattering processes in the so-called saturation region. Within this scheme the phenomenon of geometric scaling takes place: cross sections are functions only of a dimensionless combination of the relevant kinematic variables, which happens both in inclusive and diffractive cases, as in the production of vector mesons. In particular, the scaling variable is given in general by $τ= Q^2/Q_s^2$, where $Q^2$ is the photon virtuality and $Q_s$ represents the saturation scale, which drives the energy dependence and the correspondi…
Jet cross sections in deeply inelastic scattering in the case of transverse photon exchange for the production of (1+1) and (2+1) jets are calculated in next-to-leading order QCD (here the `+1' stands for the target remnant jet, which is included in the jet definition for reasons that will become clear in the main text). The jet definition scheme is based on a modified JADE cluster algorithm. The calculation of the (2+1) jet cross section is described in detail. Results for the virtual corrections as well as for the real initial- and final state corrections are given explicitly. Numerical resu…
We describe small-x_Bj deeply virtual Compton scattering measurements at HERA in terms of generalized parton distributions at leading order of perturbation series.
Recent results on Deeply Virtual Compton Scattering (DVCS) and exclusive vector meson (VM) production obtained with the H1 detector at HERA are reviewed. Emphasis is put on the transition from soft to hard diffraction and on spin dynamics.
Deeply Virtual Compton Scattering in the near forward kinematic region is the golden access to Generalized Parton Distributions. We studied the O(alphaS) corrections to the scattering amplitude for both spacelike and timelike kinematics relevant respectively to the leptoproduction of a real photon and to the photoproduction of a lepton pair. It turns out that these corrections are phenomenologically important and that the gluonic contributions are by no means negligible, even in the moderate energy range of JLab12 and of the COMPASS-II experiment at CERN.
An analysis of Deeply Virtual Compton Scattering (DVCS) is made within the colour dipole model. We compare and contrast two models for the dipole cross-section which have been successful in describing structure function data. Both models agree with the available cross section data on DVCS from HERA. We give predictions for various azimuthal angle asymmetries in HERA kinematics and for the DVCS cross section in the THERA region.
In the past decade overwhelming evidence has emerged for a conjectured duality between a wide class of gauge theories in d dimensions and string theories on asymptotically AdS_{d+1} spaces. We apply this duality to scattering processes that occur via Pomeron exchange. First we develop the Pomeron in string theory, as done by Brower, Polchinski, Strassler and Tan, showing that it naturally emerges as the Regge Trajectory of the AdS graviton. Next we apply the AdS Pomeron to the study of Deeply Virtual Compton Scattering (DVCS), and see that our model gives good results when compared to HERA dat…
We provide a universal expression of cross sections for the exclusive vector meson production and Deeply Virtual Compton Scattering (DVCS) in photon-proton and photon-nucleus interactions based on the geometric scaling phenomenon. The theoretical parameterization based on the scaling property depends only on the single variable $τ_A = Q^2/Q_{\mathrm{sat}}^2$, where the saturation scale, $Q_{\mathrm{sat}}$, drives the energy dependence and the corresponding nuclear effects. This phenomenological result describes all available data from DESY-HERA for $ρ,\,ϕ,\,J/ψ$ production and DVCS measurement…
We calculate the cross section of inclusive direct J/psi hadroproduction at next-to-leading order (NLO) within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD), including the full relativistic corrections due to the intermediate 1S_0^[8], 3S_1^[8], and 3P_J^[8] color-octet states. We perform a combined fit of the color-octet (CO) long-distance matrix elements to the transverse-momentum (p_T) distributions measured by CDF at the Fermilab Tevatron and H1 at DESY HERA and demonstrate that they also successfully describe the p_T distributions from PHENIX at BNL RHIC an…
Measurements of the deep-inelastic scattering (DIS) of leptons and nucleons, $e+p\to e+X$, allow the extraction of Parton Distribution Functions (PDFs) which describe the longitudinal momentum carried by the quarks, anti-quarks and gluons that make up the fast-moving nucleons. While PDFs provide crucial input to perturbative Quantum Chromodynamic (QCD) calculations of processes involving hadrons, they do not provide a complete picture of the partonic structure of nucleons. In particular, PDFs contain neither information on the correlations between partons nor on their transverse motion. Hard e…
We consider Deeply Virtual Compton Scattering (DVCS) on nucleons and nuclei in the framework of generalized vector meson dominance (GVMD) model. We demonstrate that the GVMD model provides a good description of the HERA data on the dependence of the proton DVCS cross section on Q^2, W (at Q^2=4 GeV^2) and t. At Q^2 = 8 GeV^2, the soft W-behavior of the GVMD model somewhat underestimates the W-dependence of the DVCS cross section due to the hard contribution not present in the GVMD model. We estimate 1/Q^2 power-suppressed corrections to the DVCS amplitude and the DVCS cross section and find th…
Diffractive parton distribution functions give the probability to find a parton in a hadron if the hadron is diffractively scattered. We provide an operator definition of these functions and discuss their relation to diffractive deeply inelastic scattering and to photoproduction of jets at HERA. We perform a calculation in the style of ``constituent counting rules'' for the behavior of these functions when the detected parton carries almost all of the longitudinal momentum transferred from the scattered hadron.
We develop the color dipole gBFKL phenomenology of a diffraction cone for photo- and electroproduction $γ^{*}N \to VN$ of heavy vector mesons (charmonium & bottonium) at HERA and in fixed target experiments. We predict a substantial shrinkage of the diffraction cone from the CERN/FNAL to the HERA range of c.m.s. energy $W$. The $Q^{2}$-controlled selectivity to the color dipole size (scanning phenomenon) is shown to lead to a decrease of the diffraction slope with $Q^{2}$ (which is supported by the available experimental data). We predict an approximate flavor independence of the diffraction s…
Deeply inelastic scattering of electrons off nuclei can determine whether parton distributions saturate at HERA energies. If so, this phenomenon will also tell us a great deal about how particles are produced, and whether they equilibrate, in high energy nuclear collisions.
Using the general notion of cross section fluctuations in hadron--nucleus scattering at high energies, we derive an expression for the cross section of incoherent $J/ψ$ photoproduction on heavy nuclei $dσ_{γA \to J/ψY}/dt$, which includes both elastic $dσ_{γp \to J/ψp}/dt$ and proton-dissociation $dσ_{γp \to J/ψY}/dt$ photoproduction on target nucleons. We find that with good accuracy, $dσ_{γA \to J/ψY}/dt$ can be expressed as a product of the sum of the $dσ_{γp \to J/ψp}/dt$ and $dσ_{γp \to J/ψY}/dt$ cross sections, which have been measured at HERA, and the common nuclear shadowing factor, wh…
We study the use of deep learning techniques to reconstruct the kinematics of the neutral current deep inelastic scattering (DIS) process in electron-proton collisions. In particular, we use simulated data from the ZEUS experiment at the HERA accelerator facility, and train deep neural networks to reconstruct the kinematic variables $Q^2$ and $x$. Our approach is based on the information used in the classical construction methods, the measurements of the scattered lepton, and the hadronic final state in the detector, but is enhanced through correlations and patterns revealed with the simulated…
Single-top-quark production via W-gluon fusion at hadron colliders provides an opportunity to directly probe the charged-current interaction of the top quark. We calculate the next-to-leading-order corrections to this process at the Fermilab Tevatron, the CERN Large Hadron Collider, and DESY HERA. Using a b-quark distribution function to sum collinear logarithms, we show that there are two independent corrections, of order 1/[ln(m_t^2/m_b^2)] and alpha_s. This observation is generic to processes involving a perturbatively derived heavy-quark distribution function at an energy scale large compa…
