We evaluate the large momentum transfer $J/ψ$ photoproduction with rapidity gaps in ultraperipheral proton-ion collisions at the LHC which provides an effective method of probing dynamics of large t elastic hard QCD Pomeron interactions. It is shown that the experimental studies of this process would allow to investigate the energy dependence of cross section of elastic scattering of a small $c\bar c$ dipole off the gluon over a wide range of invariant energies 10^3 < s_{c\bar c - gluon} < 10^6 GeV^2. The accessible energy range exceeds the one reached in γp at HERA by a factor of 10 and allows the kinematic cuts which improve greatly sensitivity to the Pomeron dynamics as compared to the HERA measurements. The cross section is expected to change by a factor \ge 20 throughout this interval and our estimates predict quite reasonable counting rates for this process with the several of the LHC detectors.
The exclusive $Υ$ photoproduction in ultraperipheral proton-nucleus and nucleus-nucleus collisions at LHC energies is being investigated using pQCD framework which constrain the gluon distribution in the proton and nuclei at low $x$. Rapidity distributions of $Υ$ photoproduction with different gluon distribution parameterization and gluon shadowing for nuclear PDFs including photon flux suppression for strong interaction, are being presented at LHC energies. Predictions done for ultraperipheral collisions at $\sqrt s$=$8.16$ TeV in pPb, and at $\sqrt s$=$5.02$ TeV in PbPb collisions which are …
Rapidity distributions of vector mesons are computed in dipole model proton-lead ultraperipheral collisions(UPCs) at the CERN Larger Hadron Collider(LHC). The dipole model framework is implemented in the calculations of cross sections in the photon-hadron interaction. The bCGC model and Boosted Gaussian wave functions are employed in the scattering amplitude. We obtain predictions of rapidity distributions of $J/ψ$ meson proton-lead ultraperipheral collisions. The predictions give a good descriptions to the experimental data of ALICE. The rapidity distributions of $ϕ$, $ω$ and $ψ(2s)$ mesons i…
We point out a significance of ultraperipheral photoproduction of vector mesons in the Coulomb field of nuclei as a means of measuring the radius of the neutral vector meson. This new contribution to the production amplitude is very small compared to the conventional diffractive amplitude, but because of large impact parameters inherent to the ultraperipheral Coulomb mechanism its impact on the diffraction slope is substantial. We predict appreciable and strongly energy dependent increase of the diffraction slope towards very small momentum transfer.The magnitude of the effect is proportional …
Photoproduction of vector mesons are computed in dipole model in proton-proton ultraperipheral collisions(UPCs) at the CERN Large Hadron Collider (LHC). The dipole model framework is employed in the calculations of vector mesons production in diffractive processes. Parameters of the bCGC model are refitted with the latest inclusive deep inelastic scattering experimental data. Employing the bCGC model and Boosted Gaussian light-cone wave function for vector mesons, we obtain prediction of rapidity distributions of $J/ψ$ and $ψ(2s)$ mesons in proton-proton ultraperipheral collisions at the LHC. …
We compare the coherent and quasielastic J/psi photoproduction in the peripheral heavy ion collisions in kinematics of RHIC. Our improved estimate of the total coherent cross section is a factor of two smaller than the earlier ones. We find that the counting rate of quasielastic J/psi photoproduction tagged by neutrons emitted due to cascading of the recoiled nucleon within the residual nucleus exceeds the rate of the coherent events. We argue that measurements of this process can be used to learn about the dynamics of color dipole-nucleon interactions in nuclei in the wide effective range of …
Based on accurate calculations of the flux of equivalent photons of the proton and heavy nuclei and the pQCD framework for the gluon distribution in the proton and nuclei, we analyze the rapidity and momentum transfer distributions of coherent $J/ψ$ photoproduction in ultraperipheral proton-Pb collisions at the LHC. We demonstrate that unlike the case of proton-proton UPCs marred by certain theoretical uncertainties and experimental limitations, after a cut excluding the region of small momentum transfers, ultraperipheral proton-Pb collisions offer a clean way to study the gluon distribution i…
Using the framework of leading order perturbative QCD along with the CTEQ6L1 gluon distribution of the proton and high-energy HERA data on the $γp \to J/ψp$ and $γp \to ψ(2S) p$ cross sections along with the corresponding H1 fit, we obtain a good description of the rapidity dependence of the cross sections of photoproduction of $J/ψ$ or $ψ(2S)$ mesons in proton--proton ultraperipheral collisions (UPCs) measured by the LHCb collaboration at the LHC. Within the same framework we also make predictions for the $pp \to pp J/ψ$ and $pp \to pp ψ(2S)$ UPC cross sections at $\sqrt{s_{NN}}=8$ and 14 TeV…
We demonstrate that study of large t vector meson photoproduction with rapidity gaps in ultraperipheral proton-ion and ion-ion collisions at LHC would allow to investigate the energy dependence of cross section of elastic scattering of a small dipole off the parton over a wide range of energies $10^3 < s_{dipole - parton} < 10^6 GeV^2$ where this cross section is expected to change by a factor $\ge 20$. The accessible energy range exceeds the one reached at HERA by a factor of 10 both in $γp$ and in $γA$ scattering. In addition, study of A-dependence of this process will allow to determine the…
We investigate the photoproduction of $ρ$ mesons in ultraperipheral heavy ion collisions at RHIC and LHC energies in the dipole approach and within two phenomenological models based on the the Color Glass Condensate (CGC) formalism. We estimate the integrated cross section and rapidity distribution for meson production and compare our predictions with the data from the STAR collaboration. In particular, we demonstrate that the total cross section at RHIC is strongly dependent on the energy behavior of the dipole-target cross section at low energies, which is not well determined in the dipole a…
Photoproduction of heavy quarks and exclusive production of vector mesons in ultraperipheral proton-nucleus and nucleus-nucleus collisions depend significantly on nuclear gluon distributions. In the present study we investigate quantitatively the extent of the applicability of these processes at the Large Hadron Collider (LHC) in constraining the shadowing component of nuclear gluon modifications.
The exclusive photoproduction of upsilon states $Υ(1S)$ and its radially excited states $Υ(2S,3S)$ is investigated in the context of ultra-peripheral collisions at the LHC energies. Predictions are presented for their production in proton-proton, proton-nucleus and nucleus-nucleus collision at the energies available at the LHC run 2. The rapidity and transverse momentum distributions are shown, and the robustness of the model is tested against the experimental results considering $ψ(1S,2S)$ and $Υ(1S)$ states. The theoretical framework considered in the analysis is the light-cone color dipole …
We present predictions for the rapidity-differential cross sections of exclusive $Υ$ photoproduction in ultraperipheral collisions (UPCs) of lead ions at the Large Hadron Collider (LHC). We work in the framework of collinear factorization at next-to-leading order (NLO) in perturbative QCD, modeling the generalized parton distributions (GPDs) through the Shuvaev transform of nuclear parton distribution functions (nPDFs). While the effects due to the GPD modeling turn out to be small, the direct NLO predictions still carry significant nPDF-originating uncertainties and depend strongly on the cho…
In this paper, we discuss the exclusive photoproduction of ground and excited states of $ψ(1S,2S)$ and $Υ(1S,2S)$ in ultraperipheral collisions (UPCs). Using the potential model in order to obtain the vector meson wave function, we find a good agreement of our calculations with data from the LHC and HERA colliders for $J/ψ(1S,2S) $ and $Υ(1S)$ in $γp$ collisions. We extend the calculations to the nuclear target case applying them to $AA$ UPCs with the use of the shadowing and finite coherence length effects fitted to the data. Our results are compared to the recent LHC data, in both incoherent…
We make predictions for cross sections of $ρ$ and $ϕ$ vector meson photoproduction in ultraperipheral Xe-Xe collisions at $\sqrt{s_{NN}}=5.44$ TeV. Analyzing the momentum transfer distribution of $ρ$ mesons in this process, we explore the feasibility of extracting the nuclear density of $^{129}$Xe, which is needed in searches for dark matter with Xenon-based detectors.
We compute cross sections for incoherent and coherent diffractive J/$Ψ$ and $Ψ(2S)$ production in ultraperipheral heavy ion collisions. The dipole models used in these calculations are obtained by fitting the HERA deep inelastic scattering data and compared with available electron-proton diffraction measurements. We obtain a reasonably good description of the available ALICE data. We find that the normalization of the ultraperipheral cross section has large model dependence, but the rapidity dependence is more tightly constrained.
A new production mechanism for the Standard Model Higgs boson in Ultraperipheral Collisions at LHC, which allows Central Exclusive Diffractive production by Double Pomeron Exchange in photon-proton processes, is presented. The Higgs boson is centrally produced by gluon fusion with two Large Rapidity Gaps emerging in the final state, being the main experimental signature for this process. As already studied for Pomeron-Pomeron and two-photon processes, the Higgs boson photoproduction is studied within this new mechanism in proton-proton ($pp$) and proton-nucleus ($pA$) collisions, where each sy…
We compute the cross section of inclusive dijet photoproduction in ultraperipheral Pb-Pb collisions at the LHC using next-to-leading order perturbative QCD. We demonstrate that our theoretical calculations provide a good description of various kinematic distributions measured by the ATLAS collaboration. We find that the calculated dijet photoproduction cross section is sensitive to nuclear modifications of parton distribution functions (PDFs) at the level of 10 to 20%. Hence, this process can be used to reduce uncertainties in the determination of these nuclear PDFs, whose current magnitude is…
Within the leading logarithmic approximation of perturbative QCD and the leading twist approach to nuclear shadowing, we compare the cross sections of photoproduction of $J/ψ$ and $ψ(2S)$ mesons on nuclei in Pb-Pb UPCs in the LHC kinematics. We find that the nuclear suppression of these cross sections due to the nuclear gluon shadowing is large and rather similar in the $J/ψ$ and $ψ(2S)$ cases.
We consider $J/ψ$ photoproduction in ion--ion ultraperipheral collisions (UPCs) at the LHC and RHIC in the coherent and incoherent quasielastic channels with and without accompanying forward neutron emission and analyze the role of nuclear gluon shadowing at small $x$, $x=10^{-4}-10^{-2}$, in these processes. We find that despite the good agreement between large nuclear gluon shadowing and the ALICE data in the coherent channel, in the incoherent channel, the leading twist approximation predicts the amount of nuclear suppression which is by approximately a factor of $1.5$ exceeds that seen in …
We present predictions for the J/psi and rho meson production in the heavy ion ultraperipheral collisions (UPC) for the current energy 2.76 TeV at the LHC. Both total cross sections and cross sections with the neutron emission from one or both nuclei are presented. We also analyse the RHIC rho meson photoproduction data and emphasize importance of these data to test the current model for nucleus break up in UPC.
We argue that the STAR data on $J/ψ$ photoproduction in $d+Au$ ultraperipheral collisions (UPCs) at the momentum transfer $t \neq 0$ primarily probes elastic and possibly nucleon-dissociative $J/ψ$ photoproduction on quasi-free nucleons, while being essentially insensitive to expectedly weak nuclear modifications of the gluon distribution in the deuteron. Analyzing the STAR detector capabilities for selection of UPC events, we explore the possibility that the contribution of nucleon-dissociative $J/ψ$ photoproduction is negligibly small and obtain a very good description of the $t$ dependence …
We present the first study of rapidity-differential cross sections of coherent exclusive $J/ψ$ photoproduction in heavy-ion ultraperipheral collisions (UPCs) at the LHC, $\text{d}σ(\text{Pb}+\text{Pb}\rightarrow \text{Pb}+J/ψ+\text{Pb})/\text{d}y$, to NLO in collinear factorisation. Taking the generalised parton distributions as their forward limit counterparts, the NLO contributions in the cross sections are quantified and we show that the real part of the amplitude and quark-PDF contributions must not be neglected. We further evaluate the uncertainties arising from the scale-choice at both L…
We present the first next-to-leading-order (NLO) perturbative QCD (pQCD) study of rapidity-differential cross sections of coherent exclusive photoproduction of $J/ψ$ mesons in heavy-ion ultraperipheral collisions (UPCs) at the LHC, $dσ/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/ψ+ \text{Pb})$. For this, we account for the photon-nucleon NLO cross sections at the forward limit, the $t$ dependence using a standard nuclear form factor, and the photon fluxes of the colliding nuclei. Approximating the generalized parton distributions with their forward-limit parton distribution functions (P…
Photoproduction of heavy quarks in ultraperipheral collisions can help elucidate important features of the physics of heavy quarks in Quantum Chromodynamics (QCD). Due to the dependence on parton distributions it can also potentially offer some constraining ability in the determination of nuclear parton distributions. In the present study we consider next-to-leading order (NLO) photoproduction of heavy quarks in ultraperipheral proton-proton (pp), proton-nucleus (pA), and nucleus-nucleus (AA) collisions at the CERN Large Hadron Collider (LHC). Total cross sections and rapidity distributions ar…
Recent data on diffractive photoproduction of dijets are analyzed within the framework of fracture functions and paying special attention to the consequences of the use of different rapidity gap definitions in order to identify diffractive events. Although these effects are found to be significant, it is shown that once they are properly taken into account, a very precise agreement between diffractive DIS and diffractive dijet photoproduction emerges without any significant hint of hard factorization breaking.
Ultraperipheral collisions in hadron colliders give new opportunites to investigate the hadron stucture through exclusive photoproduction processes. We describe the possibility of measuring the Generalized Parton Distributions in the Timelike Compton Scattering process and in the production of heavy vector meson.
In this paper we analyze the associated $ϕ$ and $J/Ψ$ photoproduction in ultraperipheral $PbPb$ collisions through the double scattering mechanism for the energies of the Large Hadron Collider (LHC) and Future Circular Collider (FCC). Our results complement a previous analysis for the $ρρ$, $J/ΨJ/Ψ$ and $ρJ/Ψ$ production. We present our predictions for the total cross sections and rapidity distributions considering the rapidity ranges covered by the ALICE and LHCb detectors, which indicate that a future experimental analysis of $ϕJ/Ψ$ final state is feasible. These results point out that the s…
We calculate the cross section of inclusive dijet photoproduction in ultraperipheral collisions (UPCs) of heavy ions at the CERN Large Hadron Collider using next-to-leading order perturbative QCD and demonstrate that it provides a good description of the ATLAS data. We study the role of this data in constraining nuclear parton distribution functions (nPDFs) using the Bayesian reweighting technique and find that it can reduce current uncertainties of nPDFs at small $x$ by a factor of 2. We also make predictions for diffractive dijet photoproduction in UPCs and examine its potential to shed ligh…
Using the Gribov-Glauber model for photon-nucleus scattering and a generalization of the vector meson dominance model for the hadronic structure of the photon, we make predictions for the cross section of incoherent $ρ$ photoproduction in Pb-Pb ultraperipheral collisions (UPCs) in the Large Hadron Collider kinematics. We find that the effect of the inelastic nuclear shadowing is significant and leads to an additional 25% suppression of the incoherent cross section. Comparing our predictions to those of the STARlight Monte Carlo framework, we observe very significant differences.
We present calculations for the incoherent photoproduction of J/$ψ$ vector mesons in ultra-peripheral heavy ion collisions (UPC) in terms of hadronic interactions. This study was carried out using the recently developed Monte Carlo model CRISP extended to include UPCs at LHC energies. A careful study of re-scattering and destruction of the J/$ψ$ particles is presented for PbPb collisions at $\sqrt{s_{NN}} = 2.76$ TeV. We have also compared our method to AuAu collisions at $\sqrt{s_{NN}} = 200$ GeV measured at RHIC.
QED radiative corrections to the cross section of diffractive electro- and photoproduction of vector mesons is calculated at HERA energies. Both semi-analytical and Monte Carlo approaches are discussed and compared.
The two gluon exchange model of the pomeron is used to compute the photoproduction reaction $γp \to Z^0 p$. The predicted cross section is too small to be observed at HERA, but may be detectable at an eventual Next Linear Collider.
Exclusive photoproduction of vector mesons in the perturbative two-gluon exchange formalism depends significantly on nucleon and nuclear gluon distributions. In the present study we calculate total cross sections and rapidity distributions of $J/ψ(1s)$, $ψ(2s)$, $Υ(1s)$, $Υ(2s)$, and $Υ(3s)$ in ultraperipheral proton-lead (pPb) and lead-lead (PbPb) collisions at the CERN Large Hadron Collider (LHC) at $\sqrt{s_{_{NN}}}=5$ TeV and $\sqrt{s_{_{NN}}}=2.76$ TeV respectively. Effects of gluon shadowing are investigated and potentials for constraining nuclear gluon modifications are discussed.
Evaluating the ratio of the exclusive vector meson photoproduction to inclusive hadron/jet production cross section in ultraperipheral heavy ion collisions
Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学）；Federal University of Rio Grande do Sul (UFRGS)（南里奥格兰德联邦大学）
We consider the diffractive photoproduction of $π^+π^- , K^+K^- , D^+D^-$ meson pairs with high masses and transverse momenta in the framework of the Söding model. The total and differential cross sections are calculated for these processes. The role of the form factors is stressed.
The cross section of the $D^*$-meson diffractive photoproduction at the HERA collider has been calculated in the framework of perturbatively motivated model for the different kinematic regions. The camparison between the different Pomeron models has been performed.
Diffractive dijet photoproduction is proposed as a probe of the off-diagonal gluon distribution and its evolution. Predictions for the transverse momentum distribution of the jets are given. Differences with DGLAP evolution are highlighted.
The comparison of photoproduction cross sections for $c\bar{c}$ and b-b(bar) in PbPb and pPb collisions can give sensitivity to nuclear shadowing effects. The photoproduction of vector mesons is even more sensitive to the underlying gluon distributions. In this study we present the cross sections and rapidity dependence of the photoproduction of heavy quarks and exclusive production of vector mesons in ultraperipheral pPb and PbPb collisions at the Large Hadron Collider at sqrt(s_NN)=5 TeV and sqrt(s_NN)=2.76$ TeV, respectively. The potentials of using these processes for constraining nuclear …
We present calculations of coherent photoproduction of vector mesons ($J/Ψ$ and $Υ$) with leading-order parton distribution functions to check new kinds of corrections of the DGLAP equations and nuclear modifications. The input gluon distribution of the proton is the dynamical parton model from the DGLAP equations with GLR-MQ-ZRS (Gribov-Levin-Ryskin, Mueller-Qiu, Zhu-Ruan-Shen) modifications. From comparison between several other gluon distribution models, we find that the dynamical gluon distribution fits with the results of meson photoproduction experiments in the high energy region. The ca…
We discuss the factorization breaking observed in diffractive dijet photoproduction by the H1 and ZEUS collaborations at HERA. By considering the effects of rapidity gap survival, hadronisation, migration and NLO contributions, we find that the observed data are compatible with theoretical expectations.
The large $t$ behaviour of the helicity amplitudes of diffractive photoproduction is estimated relying on models of the photon and meson light-cone wave functions and on the double-logarithmic approximation to the exchanged gluon interaction. The role of large-size colour dipole contributions to the photon-meson transition impact factor is discussed.
We make predictions for the cross sections of diffractive dijet photoproduction in $pp$, $pA$ and $AA$ ultraperipheral collisions (UPCs) at the LHC during Runs 1 and 2 using next-to-leading perturbative QCD. We find that the resulting cross sections are sufficiently large and, compared to lepton-proton scattering at HERA, have an enhanced sensitivity to small observed momentum fractions in the diffractive exchange, commonly denoted $z_{P}^{\rm jets}$, and an unprecedented reach in the invariant mass of the photon-nucleon system $W$. We examine two competing schemes of diffractive QCD factoriza…
The elastic differential and integrated total cross section for the exclusive $ρ^0$ photoproduction in electron-proton ($ep$) collisions are evaluated taking into account nonperturbative Pomeron exchange approach. By using three different models based on Regge phenomenology the results are compared to recent measurements by H1 Collaboration in $ep$ collisions and by the CMS collaboration from ultraperipheral proton-lead collisions. The analysis is expanded by calculating the coherent nuclear cross section, $σ(γA\rightarrow ρ^0 A)$, which is applied to $ρ^0$ production in ultraperipheral lead-l…
We present a detailed study of vector meson photoproduction in ultraperipheral heavy ion collisions (UPCs). Using the dipole model, we develop a framework for the joint impact parameter and transverse momentum dependent cross sections. We compute the unpolarized cross section and $\cos 2ϕ$ azimuthal angular correlation for $ρ^0$ photoproduction with $ϕ$ defined as the angle between the $ρ^0$'s transverse momentum and its decay product pion meson's transverse momentum. Our result on unpolarized coherent differential cross section gives excellent description to the STAR experimental data. A firs…
We study spin asymmetries in diffractive $Q \bar Q$ and vector meson production which are sensitive to the spin-dependent part of the two-gluon-nucleon coupling. It is found that the $A_{ll}$ and $A_{lT}$ asymmetry in diffractive reactions can be used to study polarized gluon distributions of the proton.
The inclusive $J/Ψ$ production by direct and resolved photoproduction in the $γ$p scattering is calculated based on the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, which is in good agreement with the experimental data of total cross section distribution of heavy quarkonium production at HERA. Then we extend the formalism including the direct and resolved photoproduction processes to resolved pomeron model to study the heavy quarkonium photoproduction at the LHC energies. We present the predictions of rapidity and transverse momentum distributions of the inclusive di…
We make predictions for the cross sections of coherent photoproduction of $ρ$, $ϕ$, $J/ψ$, $ψ(2S)$, and $Υ(1S)$ mesons in Pb-Pb ultraperipheral collisions (UPCs) at $\sqrt{s_{NN}}=5.02$ TeV in the kinematics of run 2 at the Large Hadron Collider extending the approaches successfully describing the available Pb-Pb UPC data at $\sqrt{s_{NN}}=2.76$ TeV. Our results illustrate the important roles of hadronic fluctuations of the photon and inelastic nuclear shadowing in photoproduction of light vector mesons on nuclei and the large leading twist nuclear gluon shadowing in photoproduction of quarkon…
We evaluate the Psi' to J/Psi ratio in diffractive photoproduction in a light-cone framework, using charmonium wave functions extracted from non-relativistic potential models. Contrary to current belief, we find that the best estimate for the ratio is a factor 2 to 5 below the data. The measured ratio constrains the distribution of the charm quark-antiquark component of the charmonium light-cone wave function and indicates that it is more compact than in potential models. We predict that the inelastic photoproduction ratio will be bigger than the elastic one, and will equal that measured in ha…
We argue that study of total cross section of photoabsorption and coherent photoproduction of $ρ,ρ^{\prime}$-mesons in ultraperipheral heavy ion collisions (UPC) is effective method to probe onset of black body limit(BBL) in the soft and hard QCD interactions. We illustrate the expected features of the onset of BBL using generalized vector dominance model. We show that this model describes very well $ρ$-meson coherent photoproduction at $6 \leq E_γ \leq 10 GeV$. In the case of $ρ$-meson production we find a UPC cross section which is a factor $\sim 1.5 $ larger than the one found by Klein and …
In this letter we study the diffractive photoproduction of heavy quarks in hadronic (pp/pA/AA) interactions for Tevatron and LHC energies. The integrated cross section and rapidity distribution for the process h_1 h_2 --> h_1 h_2 QQBAR (h_i = p,A and Q = c,b) are estimated using the Color Glass Condensate (CGC) formalism. Our results indicate that this production channel has larger cross sections than the competing reactions of double diffractive production and coherent AA reactions initiated by two-photon collisions.
Ultraperipheral collisions (UPCs) of protons and nuclei are important for the study of the photoproduction of vector mesons and exotic states. The photoproduction of vector mesons in the pentaquark resonance channel in $p\mbox{-}Au$ UPCs at the Relative Heavy Ion Collider (RHIC) and $p$-$Pb$ UPCs at the Large Hadron Collider (LHC) is investigated by employing STARlight package. The cross sections of vector mesons via pentaquark state resonances channel are obtained using effective Lagrangian method. The pseudo-rapidity and rapidity distributions of $J/ψ$ and $Υ(1S) $ are given for $p\mbox{-}Au…
Diffractive photoproduction of rho, phi and J/psi was studied in the BFKL approach to hard colour singlet exchange. Differential cross sections, the energy dependence and spin density matrix elements were calculated and compared to data from HERA. The overall description of data is reasonably good, except of the single flip amplitude which has the wrong sign. Importance of chiral odd components of the photon is stressed.
Exclusive photoproduction of dileptons, gamma N ->l+l- N, is and will be measured in ultraperipheral collisions at hadron colliders. We demonstrate that the timelike deeply virtual Compton scattering (TCS) mechanism gamma q -> l+l- q, where the lepton pair comes from the subprocess gamma q -> gamma* q, dominates in some accessible kinematical regions, thus opening a new way to study generalized parton distributions (GPD) in the nucleon at small skewedness.
