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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 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

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