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Generalized Parton Distributions (GPDs) are nowadays the object of an intense effort of research, in the perspective of understanding nucleon structure. They describe the correlations between the longitudinal momentum and the transverse spatial position of the partons inside the nucleon and they can give access to the contribution of the orbital momentum of the quarks to the nucleon spin. Deeply Virtual Compton scattering (DVCS), the electroproduction on the nucleon, at the quark level, of a real photon, is the process more directly interpretable in terms of GPDs of the nucleon. Depending on the target nucleon (proton or neutron) and on the DVCS observable extracted (cross-sections, target- or beam-spin asymmetries, etc.), different sensitivity to the various GPDs for each quark flavor can be exploited. This article is focused on recent promising results, obtained at Jefferson Lab, on cross-sections and asymmetries for DVCS, and their link to GPDs. These data open the way to a “tomographic” representation of the structure of the nucleon, allowing the extraction of transverse-space densities of the quarks at fixed longitudinal momentum. The extensive experimental program to measure GPDs at Jefferson Lab with the 12 GeV-upgraded electron accelerator and the complementary detectors that will be housed in three experimental Halls (A, B and C), will also be presented.

A new numerical method, which is called the General Particle Dynamics (GPD) method, is proposed to investigate the zonal disintegration mechanism of isotropic rock masses around a deep circular tunnel subjected to dynamic unloading as well as the stress distributions. A constitutive model based on the GPD method is developed to simulate the zonal disintegration phenomenon in deep rock masses. The number and size of fractured and nonfractured zones are determined using the nonlinear unified strength criterion. It is shown from the numerical results that the dynamic loads and high in situ stress are two dominant factors for the occurrence of zonal disintegration.

Our original suggestion to investigate exclusive π⁰ electroproduction as a method for extracting from data the tensor charge, transversity, and other quantities related to chiral odd generalized parton distributions is further examined. We now explain the details of the process: i) the connection between the helicity description and the cartesian basis; ii) the dependence on the momentum transfer squared, Q², and iii) the angular momentum, parity, and charge conjugation constraints (J^PC quantum numbers).

We argue that due to parity constraints, the helicity combination of the purely momentum space counterparts of the Wigner distributions — the generalized transverse momentum distributions — that describes the configuration of an unpolarized quark in a longitudinally polarized nucleon, can enter the deeply virtual Compton scattering amplitude only through matrix elements involving a final state interaction. The relevant matrix elements in turn involve light cone operators projections in the transverse direction, or they appear in the deeply virtual Compton scattering amplitude at twist three. Orbital angular momentum or the spin structure of the nucleon was a major reason for these various distributions and amplitudes to have been introduced. We show that twist three contributions to deeply virtual Compton scattering provide observables related to orbital angular momentum.

Our original suggestion to investigate exclusive π⁰ electroproduction as a method for extracting the tensor charge, transversity, and other quantities related to chiral odd generalized parton distributions from cross section and asymmetry data is reviewed. We explain some of the details of the process: i) the connection between the helicity description and the cartesian basis; ii) the dependence on the momentum transfer squared, Q², and iii) the angular momentum, parity, and charge conjugation constraints (J^PC quantum numbers).

We discuss an holographic soft wall model to describe nucleon properties. We pay special attention to nucleon spectrum, GPDs in the skewness case for nucleons and electroproduction of the N (1440) Roper resonance in soft-wall AdS/QCD.

We compute the pion Generalized Parton Distribution (GPD) in a valence dressed quarks approach. We model the Mellin moments of the GPD using Ansätze for Green functions inspired by the numerical solutions of the Dyson-Schwinger Equations (DSE) and the Bethe-Salpeter Equation (BSE). Then, the GPD is reconstructed from its Mellin moment using the Double Distribution (DD) formalism. The agreement with available experimental data is very good.

The concept of Generalized Parton Distributions (GPDs) combines two-dimensional spatial information given by form factors, with longitudinal momentum information from Parton Distribution Functions. GPDs provide comprehensive description of the nucleon structure involving a wealth of new information. For instance, according to Ji’s sum rule, the GPDs $H$ and $E$ enable access to the total angular momenta of quarks, antiquarks and gluons. While $H$ can be approached using measurements of electroproduction cross sections, asymmetry measurements in hard exclusive meson production off transversely polarized targets can help to constrain the GPD $E$ and chiral-odd GPDs.

In 2007 and 2010 the COMPASS experiment at CERN collected data by scattering a $160\mathrm{\text{GeV}}/c$ muon beam off a transversely polarized NH3 target. Exclusive vector-meson production $\mu +p\to {\mu }^{\prime }+p+V$ with a ${\rho }^0$ or $\omega$ meson in the final state is studied and five single-spin and three double-spin azimuthal asymmetries are measured.

Enlarging the set of hard exclusive reactions to be studied in the framework of QCD collinear factorization opens new possibilities to access generalized parton distributions (GPDs). We studied the photoproduction of a large invariant mass photon-photon or photon-meson pair in the generalized Bjorken regime which may be accessible both at JLab and at the EIC.

Weeks V and VI of the INT program 2018 were dedicated to physics opportunities at a future Electron-Ion Collider. Discussions were wide ranging and included topics such as short-range correlation, jets physics in deep inelastic scattering, nuclear PDFs, TMDs, and GPDs as well as small-x helicity distributions, non-linear small-x evolution equations, diffraction and particle production and correlations.

Besides a GPD based description, the collinear factorisation theorem of QCD also allows a TDA based description of the hard exclusive pion electroproduction. Both descriptions provide access to different kinematic regions and therefore give us insights into different aspects of the 3 dimensional nucleon structure. To understand the complete reaction mechanism and the validity of the different models, experimental studies over the full kinematic range have to be performed. In this work measurements of the beam-spin asymmetry have been performed over a wide range of kinematics in the deep inelastic regime for the hard exclusive e p → e n π⁺ reaction using the CEBAF Large Acceptance Spectrometer (CLAS) and a 5.5 GeV polarized electron beam at Jefferson Lab (JLAB). The ϕ dependence of the BSA as well as the Q², x_B and t dependence of the extracted moments will be presented. A clear sign change of the BSA can be observed between pions emitted in forward and backward direction with a smooth transition around 90° in CM.

Seven years of experimental efforts at Jefferson Lab on Deeply Virtual Compton Scattering yielded very significant results such as a strong indication for the handbag dominance (i.e. scaling) even et low energy, the first comparisons to models and a large data sample to constrain their free parameters and even a first model-dependent extraction of the total angular momentum carried by quarks. These proceedings try to summarize the information collected so far without going into details, and in a semi-chronological fashion.

Hard exclusive reactions are the tool to learn about generalized parton distributions, which provide a more complete parametrization of the nucleon than the ordinary parton distribution functions. Recent measurements by the HERMES collaboration of the exclusive production of photons, i.e., Deeply-Virtual Compton Scattering, are summarized and compared to model calculations, focusing on the measurements and model comparisons relevant to the extraction of quark orbital angular momentum and on the measurements on heavy nuclei.

The beam spin asymmetries of the reaction in the Bjorken regime were measured over a wide kinematical domain using the CLAS detector and a new lead-tungstate calorimeter. Through the interference of the Bethe-Heitler process with Deeply Virtual Compton Scattering, those asymmetries provide constraints for the nucleon Generalized Parton Distributions models. The observed shapes are in agreement with twist-2 dominance predictions.

Exclusive π⁰ electroproduction from nucleons can be related to transversity, the tensor charge, and other quantities related to transversity. This process isolates C-parity odd and chiral odd combinations of t-channel exchange quantum numbers. In a hadronic picture the meson production amplitudes for intermediate energy and Q² are determined by C–odd Regge exchanges with final state interactions. The helicity structure for this C-odd process relates to the quark helicity flip, or chiral odd generalized parton distributions (GPDs). Various cross sections and asymmetries will be sensitive to the transversity.

Exclusive meson leptoproduction from nucleons in the deeply virtual exchanged boson limit can be described by generalized parton distributions (GPDs). Including spin dependence in the description requires 8 independent quark-parton and gluon-parton functions. The chiral even subset of 4 quark-nucleon GPDs are related to nucleon form factors and to parton distribution functions. The chiral odd set of 4 quark-nucleon GPDs are related to transversity, the tensor charge, and other quantities related to transversity. Different meson or photon production processes access different combinations of GPDs. This is analyzed in terms of t-channel exchange quantum numbers, J^PC and it is shown that pseudoscalar production can isolate chiral odd GPDs. There is a sensitive dependence in various cross sections and asymmetries on the tensor charge of the nucleon and other transversity parameters. In a second section, analyticity and completeness are shown to limit the partonic interpret ation of the GPDs in the ERBL region.