New framework for extracting GPDs from exclusive photon electroproduction

Hard exclusive processes, such as deep electroproduction of photons and mesons off nuclear targets, could give access, in the coherent channel, to nuclear generalized parton distributions (GPDs). Here, a realistic microscopic calculation of the unpolarized quark GPD H_q of the 3He nucleus is reviewed. In Impulse Approximation, H_q is obtained as a convolution between the GPD of the internal nucleon and the non-diagonal spectral function, describing properly Fermi motion and binding effects. The obtained formula has the correct limits. Nuclear effects, evaluated by a modern realistic potential, are found to be larger than in the forward case. In particular, they increase with increasing the momentum transfer and the asymmetry of the process. Another feature of the obtained results is that the nuclear GPD cannot be factorized into a Delta^2-dependent and a Delta^2-independent term, as suggested in prescriptions proposed for finite nuclei. The dependence of the obtained GPDs on different realistic potentials used in the calculation shows that these quantities are sensitive to the details of nuclear structure at short distances.

Hadron structure: the fundamental physics to access via GPDs

Measurements of the deep-inelastic scattering (DIS) of leptons and nucleons, e + p → 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 informati on on the correlations between partons nor on their transverse motion. Hard exclusive processes, in which the nucleon remains intact, have emerged in recent years as prime candidates to complement this essentially one dimentional picture. The simplest exclusive process is the deeply virtu al Compton scattering (DVCS) or exclusive production of real photon, e+ p → e+ γ + p. This process is of particular interest as it has both a clear experimental signature and is calculable in per turbative QCD. The DVCS reaction can be regarded as the elastic scattering of the virtual photon o ff the proton via a colourless exchange, producing a real photon in the final state [1, 2]. In the Bjorke n scaling regime, QCD calculations assume that the exchange involves two partons, having different longitudinal and transverse momenta, in a colourless configuration. These unequal momen ta or skewing are a consequence of the mass difference between the incoming virtual photon and the outgoing real photon. This skewedness effect can be interpreted in the context of generalised parton distributions (GPDs) [3]. In this proceeding, we examine typical measurements from HERA and prospects for COMPASS at CERN [4], that can bring new insights on the quarks/gluons imaging of the nucleon.

To leading order approximation, the physical content of generalized parton distributions (GPDs) that is accessible in deep virtual electroproduction of photons or mesons is contained in their value on the cross-over trajectory. This trajectory separates the t-channel and s-channel dominated GPD regions. The underlying Lorentz covariance implies correspondence between these two regions through their relation to GPDs on the cross-over trajectory. This point of view leads to a family of GPD sum rules which are a quark analogue of finite energy sum rules and it guides us to a new phenomenological GPD concept. As an example, we discuss the constraints from the JLab/Hall A data on the dominant u-quark GPD H. The question arises whether GPDs are governed by some kind of holographic principle.

A realistic microscopic calculation of the unpolarized quark Generalized\nParton Distribution (GPD) $H_q^3$ of the $^3He$ nucleus is presented. In\nImpulse Approximation, $H_q^3$ is obtained as a convolution between the GPD of\nthe internal nucleon and the non-diagonal spectral function, describing\nproperly Fermi motion and binding effects. The proposed scheme is valid at low\nvalues of $\\Delta^2$, the momentum transfer to the target, the most relevant\nkinematical region for the coherent channel of hard exclusive processes. The\nobtained formula has the correct forward limit, corresponding to the standard\ndeep inelastic nuclear parton distributions, and first moment, giving the\ncharge form factor of $^3He$. Nuclear effects, evaluated by a modern realistic\npotential, are found to be larger than in the forward case. In particular, they\nincrease with increasing the momentum transfer when the asymmetry of the\nprocess is kept fixed, and they increase with the asymmetry at fixed momentum\ntransfer. Another relevant feature of the obtained results is that the nuclear\nGPD cannot be factorized into a $\\Delta^2$-dependent and a\n$\\Delta^2$-independent term, as suggested in prescriptions proposed for finite\nnuclei. The size of nuclear effects reaches 8 % even in the most important part\nof the kinematical range under scrutiny. The relevance of the obtained results\nto study the feasibility of experiments is addressed.\n

Kaon generalized parton distributions (GPDs) and the leading Fock state light-front wave functions are investigated in the framework of Nambu–Jona-Lasinio model with proper time regularization. In addition, we compared the form factors, parton distribution functions, and generalized form factors obtained from them, respectively. The first Mellin moments of GPDs result in the form factors of local currents. The second Mellin moments of vector GPDs are related to gravitational form factors, the quark mass distribution theta _2 and the quark pressure distribution theta _1. When taking a Fourier transform of GPDs in impact parameter space, we can get the mean-squared impact parameter for the quarks of the kaon: langle {varvec{b}}_{bot }^2rangle _K^u=0.149 fm^2, langle {varvec{b}}_{bot }^2rangle _K^s=0.088 fm^2. This means that the kaon s quark is nearer to the center of transverse momentum than the u quark. We also give the light-cone energy radius for the quarks of the kaon from the mass distribution theta _2: r_{E,LC}^{u,K}=0.187 fm, r_{E,LC}^{s,K}=0.167 fm, and the light-cone charge radius from quark form factors of the kaon: r_{c,LC}^{u,K}=0.390 fm, r_{c,LC}^{s,K}=0.296 fm, which means that the s quark has a smaller extent than the u quark. The light-front transverse-spin distributions rho _u^1left( {varvec{b}}_{bot },{varvec{s}}_{perp }right) and rho _u^2left( {varvec{b}}_{bot },{varvec{s}}_{perp }right) show distortions, the average shift are langle b_{bot }^yrangle _1^u=0.116 fm and langle b_{bot }^yrangle _2^u=0.083 fm. On the kinematic domain associated with the valence-quark dominance, the unpolarized Wigner distribution from light-front wave functions is sharply peaked. It extends as the transverse position variable increases in magnitude and has a domain of negative support. Through the comparison of distributions from the two methods, we find that they give the same multi-dimensional mapping of the kaon in the Nambu–Jona-Lasinio model.

Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive electroproduction processes require a generalization of the usual parton distributions for the case when long-distance information is accumulated in nondiagonal matrix elements of quark and gluon light-cone operators. I describe two types of nonperturbative functions parametrizing such matrix elements: double distributions and skewed parton distributions. I discuss their general properties, relation to the usual parton densities and form factors, evolution equations for both types of generalized parton distributions (GPD), models for GPDs and their applications in virtual and real Compton scattering.

Deeply virtual exclusive processes probe the internal structure of nucleons through measurements of structure functions and their ratios, which are sensitive to the chiral-even generalized parton distributions (GPDs) and the chiral-odd transversity GPDs. The GPDs encode correlations of parton distributions in longitudinal momentum space and transverse impact parameter space and are accessible through the measurements of the xB and t dependence of meson production. The wide kinematic coverage of CLAS detector allowed measurements of exclusive π0 electroproduction in full azimuthal range. The target and double spin asymmetries for the deeply virtual exclusive π0 electroproduction were measured for the first time in the DIS region. The experiment was carried out at Hall B, Jefferson Lab using the longitudinally polarized electron beam with energy of up to 6 GeV and a dynamically polarized NH3 target with spins of free protons aligned along the beam axis. All four final-state particles from exclusive channel, electron, proton and two photons from π0 decay, were identified. The asymmetries were fitted according to their angular modulations in the hadronic center-of-mass system, and their moments were extracted. The data comparison with two handbag-based calculations involving the contribution from both chiral-even and chiral-odd GPDs was performed in wide kinematic range. The applicability of a formalism based on generalized parton distributions within the framework of modified perturbative approach is discussed.

Generalized parton distributions of hadrons with composite constituents

In this paper, both the unpolarized and the polarized $\rho$ meson generalized parton distributions are investigated in the framework of the Nambu--Jona-Lasinio model using proper time regularization scheme. The symmetry properties of $\rho$ meson generalized parton distributions are checked. The three independent distribution functions in deep inelastic scattering, $F_1(x)$, $b_1(x)$ and $g_1(x)$, and the Sachs-like charge, magnetic, and quadruple form factors $G_C(t)$, $G_M(t)$ and $G_Q(t)$, which are the first Mellin moments of unpolarized generalized parton distributions are obtained. In addition, the $u$ quark axial vector form factors $\tilde{F}_1^u(t)$ and $\tilde{F}_2^u(t)$ related to the axial currents from the polarized generalized parton distributions are studied. The impact parameter dependent parton distribution functions, which are the two-dimensional Fourier transform of generalized parton distributions are studied, too. The obtained $\rho$ meson generalized parton distributions satisfy the required properties well.

Pion generalized parton distributions are calculated within the framework of the Nambu–Jona-Lasinio model using different regularization schemes, including the proper time regularization scheme, the three-dimensional (3D) momentum cutoff scheme, the four-dimensional momentum cutoff scheme, and the Pauli-Villars regularization scheme. Furthermore, we check the theoretical constraints of pion generalized parton distributions required by the symmetries of quantum chromodynamics in different regularization schemes. The diagrams of pion parton distribution functions are plotted, in addition, we evaluate the Mellin moments of generalized parton distributions, which are related to the electromagnetic and gravitational form factors of pion. Pion generalized parton distributions are continuous but not differential at , when considering the effect of the contact contribution term, generalized parton distributions become not continuous at in all the four regularization schemes. Generalized parton distributions in impact parameter space are considered, the width distribution of u quark in the pion and the mean-squared are calculated. The light-front transverse-spin distributions are studied when quark polarized in the light-front-transverse direction, the transverse-spin density is no longer symmetric around , the peaks shift to , we compare the average transverse shift and in different regularization schemes. The light-cone energy radius and the light-cone charge radius are also evaluated, we found that in the proper time regularization scheme the values of these quantities were the largest, in the 3D momentum cutoff scheme they were the smallest.

The measurement of the production of exclusive vector mesons, pions and photons in deep-inelastic lepton scattering gives a means to access the recently introduced generalized parton distributions (GPDs). Recent data on these exclusive reactions, collected by the HERMES collaboration at DESY, are compared to calculations which are based on a description of the reactions in terms of GPDs. In addition, prospects of a new HER MES recoil detector which will clearly identify exclusive events in the next running period are presented.

The high energy polarised muon beam available at CERN, with positive or negative charge, makes COMPASS a unique place for studies of General Parton Distributions (GPDs). The dedicated COMPASS GPD program started in 2012 with commissioning of a new long liquid hydrogen target and new detectors, such as the large recoil particle detector CAMERA and the large-angle electromagnetic calorimeter. It was followed by a short pilot ‘DVCS run’. The first results on DVCS and exclusive π0 channels have been obtained. From the sum of cross sections measured with positive and negative beam polarities the pure DVCS cross-section and its dependence on the squared four-momentum transfer t have been extracted. It allowed a first estimate of the transverse size of the partonic distribution of the nucleon in a range of intermediate xBj with a mean xBj value of 0.056. We report also on the absolute value of the cross section for exclusive π0 production and its dependence on t and azimuthal angle ϕ between the scattering plane and π0 production plane. These measurements are aiming to constrain the GPDs, in particular chiral-odd (transversity) GPDs. The full data taking for the GPD program approved within the COMPASS-II proposal continues in 2016 and 2017.

In this paper, we present our QCD analysis of the Nucleon Form Factors presented by JLab to extract a new parameterization for the valence Generalized Parton Distributions (GPDs), [Formula: see text] and [Formula: see text]. We choose simple parameterizations for [Formula: see text] and [Formula: see text] dependence of GPDs at zero skewness. These free parameters of the model are then obtained using old and new data of nucleon’s elastic electromagnetic form factors (FFs) from JLAB. We have also used the “Hessian method” to perform a careful estimation of the uncertainties for the nucleon GPDs and corresponding observables originate from experimental errors. We also calculate the parton distribution functions (PDFs) in Impact parameter space to show the 3D structure of the Nucleon. We also calculated the proton and the neutron charge densities [Formula: see text]. We show that there is a highly localized negative charge near the center of the neutron and it is because of the negatively charged down quarks dominating the high momentum quarks in the neutron. Finally using the obtained Dirac’s FF, we had an estimation for the proton charge radius. The predictions based on the obtained nucleon GPDs are in good agreement with all available experimental data and other phenomenological models.

It has been recently proposed to study coherent deeply virtual Compton scattering (DVCS) off 3He nuclei to access neutron generalized parton distributions (GPDs). In particular, it has been shown that, in Impulse Approximation (IA) and at low momentum transfer, the sum of the quark helicity conserving GPDs of 3He, H and E, is dominated by the neutron contribution. This peculiar result makes the 3He target very promising to access the neutron information. We present here the IA calculation of the spin dependent GPD H See Formula in PDF of 3He. Also for this quantity the neutron contribution is found to be the dominant one, at low momentum transfer. The known forward limit of the IA calculation of H See Formula in PDF , yielding the polarized parton distributions of 3He, is correctly recovered. The extraction of the neutron information could be anyway non trivial, so that a procedure, able to take into account the nuclear effects encoded in the IA analysis, is proposed. These calculations, essential for the evaluation of the coherent DVCS cross section asymmetries, which depend on the GPDs H,E and H See Formula in PDF , represent a crucial step for planning possible experiments at Jefferson Lab.