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The strong force which binds hadrons is described by the theory of quantum chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the parton distribution functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by generalized parton distributions (GPDs) and transverse-momentum-dependent parton distribution functions (TMD PDFs). In our previous report Lin et al. (2018), we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice-QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and lattice-QCD communities, and yield improvements for these generalized PDFs.

The strong force which binds hadrons is described by the theory of Quantum Chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the Parton Distribution Functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by Generalized Parton Distributions (GPDs) and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs). In our previous review, we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and Lattice QCD communities, and yield improvements for these generalized PDFs., 2020 PDFLattice Report, 64 pages, 34 figures

Exclusive photoproduction of a $\gamma\,\pi^\pm$ pair in the kinematics where the pair has a large invariant mass and the final nucleon has a small transverse momentum is described in the collinear factorization framework. The scattering amplitude is calculated at leading order in $\alpha_s$ and the differential cross sections for the process are estimated in the kinematics of the JLab~12-GeV experiments. The order of magnitude of the predicted cross-sections seems sufficient for a dedicated experiment to be performed. The process turns out to be very sensitive to the axial generalized parton distribution combination $\tilde{H}_u - \tilde{H}_d$., Comment: 44 pages, 16 figures. arXiv admin note: substantial text overlap with arXiv:1609.03830

Introduced in the mid 90’s, Generalized Parton Distributions (GPDs) are now a key element in the study of the nucleon internal structure. GPDs are a generalization of Form Factors and Parton Distribution Functions. They encapsulate both spatial and momentum distributions of partons inside a nucleon, allowing to perform its three-dimensional tomography. Furthermore, they allow to derive the total orbital angular momentum of quarks through the Ji sum rule, which is a crucial point to unravel the nucleon spin structure. By providing a more complete description of hadrons in terms of quarks and gluons, a deeper understanding of Quantum Chromodynamics can be reached.GPDs are experimentally accessible through deeply exclusive electro-production processes, and one of the simplest channels available is Deeply Virtual Compton Scattering (DVCS). A worldwide experimental program was started in the early 2000’s to extract these GPDs. The DVCS experiment E12-06-114 performed at Jefferson Laboratory Hall A (Virginia, USA) between 2014 and 2016, is encompassed in this program. The aim of this experiment is to extract with high precision the DVCS helicity-dependent cross sections as a function of the momentum transfer Q², for fixed values of the Bjorken variable xBj, on a proton target. The recent upgrade of the accelerator facility to 12 GeV allows to cover a larger Q² range than in previous measurements and probe yet unexplored kinematic regions, while the polarized electron beam allows the separation of the contributions from the real and imaginary parts of the DVCS amplitude to the total cross section. In this document, a brief summary of the worldwide experimental program for the study of GPDs will be provided, followed by a description of the E12-06-114 apparatus and data analysis. Finally, the results of the unpolarized and polarized cross-section measurements are presented and compared to a few selected models.; Introduites au milieu des années 90, les Distributions Généralisées de Partons (GPD) sont aujourd'hui un élément clé dans l'étude de la structure interne du nucléon. Les GPD sont la généralisation des Facteurs de Forme et des Fonctions de Distribution de Partons. Elles englobent la distribution spatiale et la distribution en impulsion des partons à l'intérieur du nucléon, ce qui permet d'en effectuer une tomographie en trois dimensions. De plus, elles permettent d'obtenir le moment orbital angulaire total des quarks grâce à la règle de somme de Ji, ce qui est un élément crucial dans l'élucidation de l'énigme de la structure en spin du nucléon. En décrivant de manière plus complète la structure des hadrons en termes de quarks et gluons, il est possible d'approfondir notre compréhension de la Chromodynamique Quantique. Les GPD sont accessibles expérimentalement à travers les processus d'électro-production exclusifs profonds, et l'un des canaux les plus simples est la Diffusion Compton Profondément Virtuelle (DVCS). Un programme expérimental mondial a été lancé au début des années 2000 afin d'extraire ces GPD. L'expérience DVCS E12-06-114 qui a été effectuée dans le Hall A du Jefferson Laboratory (Virginie, Etats-Unis) entre 2014 et 2016 est incluse dans ce programme. Le but de cette expérience est de mesurer avec grande précision la section efficace DVCS dépendante de l'hélicité en fonction du transfert d'impulsion Q², pour des valeurs fixes de la variable de Bjorken xBj, sur une cible de proton. La récente amélioration à 12 GeV de l'accélérateur permet d'obtenir un bras de levier en Q² plus important que lors des expériences précédentes et de sonder des régions cinématiques encore inexplorées, tandis que le faisceau polarisé d'électrons permet de séparer les contributions des parties réelles et imaginaires de l'amplitude DVCS à la section efficace totale. Dans ce document, un bref résumé du programme expérimental mondial sur l'étude des GPD va être fourni, suivi par la description de l'appareillage et l'analyse des données de l'expérience E12-06-114. Enfin, les résultats des mesures de sections efficaces polarisées et non-polarisées sont présentés et comparés à une sélection de modèles.

Introduced in the mid 90’s, Generalized Parton Distributions (GPDs) are now a key element in the study of the nucleon internal structure. GPDs are a generalization of Form Factors and Parton Distribution Functions. They encapsulate both spatial and momentum distributions of partons inside a nucleon, allowing to perform its three-dimensional tomography. Furthermore, they allow to derive the total orbital angular momentum of quarks through the Ji sum rule, which is a crucial point to unravel the nucleon spin structure. By providing a more complete description of hadrons in terms of quarks and gluons, a deeper understanding of Quantum Chromodynamics can be reached.GPDs are experimentally accessible through deeply exclusive electro-production processes, and one of the simplest channels available is Deeply Virtual Compton Scattering (DVCS). A worldwide experimental program was started in the early 2000’s to extract these GPDs. The DVCS experiment E12-06-114 performed at Jefferson Laboratory Hall A (Virginia, USA) between 2014 and 2016, is encompassed in this program. The aim of this experiment is to extract with high precision the DVCS helicity-dependent cross sections as a function of the momentum transfer Q², for fixed values of the Bjorken variable xBj, on a proton target. The recent upgrade of the accelerator facility to 12 GeV allows to cover a larger Q² range than in previous measurements and probe yet unexplored kinematic regions, while the polarized electron beam allows the separation of the contributions from the real and imaginary parts of the DVCS amplitude to the total cross section. In this document, a brief summary of the worldwide experimental program for the study of GPDs will be provided, followed by a description of the E12-06-114 apparatus and data analysis. Finally, the results of the unpolarized and polarized cross-section measurements are presented and compared to a few selected models., Introduites au milieu des années 90, les Distributions Généralisées de Partons (GPD) sont aujourd'hui un élément clé dans l'étude de la structure interne du nucléon. Les GPD sont la généralisation des Facteurs de Forme et des Fonctions de Distribution de Partons. Elles englobent la distribution spatiale et la distribution en impulsion des partons à l'intérieur du nucléon, ce qui permet d'en effectuer une tomographie en trois dimensions. De plus, elles permettent d'obtenir le moment orbital angulaire total des quarks grâce à la règle de somme de Ji, ce qui est un élément crucial dans l'élucidation de l'énigme de la structure en spin du nucléon. En décrivant de manière plus complète la structure des hadrons en termes de quarks et gluons, il est possible d'approfondir notre compréhension de la Chromodynamique Quantique. Les GPD sont accessibles expérimentalement à travers les processus d'électro-production exclusifs profonds, et l'un des canaux les plus simples est la Diffusion Compton Profondément Virtuelle (DVCS). Un programme expérimental mondial a été lancé au début des années 2000 afin d'extraire ces GPD. L'expérience DVCS E12-06-114 qui a été effectuée dans le Hall A du Jefferson Laboratory (Virginie, Etats-Unis) entre 2014 et 2016 est incluse dans ce programme. Le but de cette expérience est de mesurer avec grande précision la section efficace DVCS dépendante de l'hélicité en fonction du transfert d'impulsion Q², pour des valeurs fixes de la variable de Bjorken xBj, sur une cible de proton. La récente amélioration à 12 GeV de l'accélérateur permet d'obtenir un bras de levier en Q² plus important que lors des expériences précédentes et de sonder des régions cinématiques encore inexplorées, tandis que le faisceau polarisé d'électrons permet de séparer les contributions des parties réelles et imaginaires de l'amplitude DVCS à la section efficace totale. Dans ce document, un bref résumé du programme expérimental mondial sur l'étude des GPD va être fourni, suivi par la description de l'appareillage et l'analyse des données de l'expérience E12-06-114. Enfin, les résultats des mesures de sections efficaces polarisées et non-polarisées sont présentés et comparés à une sélection de modèles.

Based on the collinear factorization approach, we present a comprehensive perturbative next-to-leading (NLO) analysis of deeply virtual meson production (DVMP). Our representation in conformal Mellin space can serve as basis for a global fitting procedure to access generalized parton distributions from experimental measurements of DVMP and deeply virtual Compton scattering (DVCS). We introduce a rather general formalism for the evaluation of conformal moments that can be developed further beyond the considered order. We also confirm previous diagrammatical findings in the pure singlet quark channel. Finally, we use the analytic properties of the hard scattering amplitudes to estimate qualitatively the size of radiative corrections and illustrate these considerations with some numerical examples. The results suggest that global NLO GPD fits, including both DVMP and DVCS data, could be more stable than often feared., 125 pages, 7 figures, 8 tables