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Generalized parton distributions can be used to obtain information about the dependence of parton distributions on the impact parameter. Potential consequences for T-odd single-spin asymmetries are discussed.

The investigation of the partonic degrees of freedom beyond collinear approximation (3D description) has been gained increasing interest in the last decade. At the HERMES experiment, azimuthal asymmetries in hard exclusive reactions and in semi-inclusive deep-inelastic scattering of electrons and positrons off a (polarized) hydrogen and deuterium target have been measured. Such asymmetries provide new insights on crucial aspects of the parton dynamics. By measuring various hadron types in the initial and final states, flavor sensitivity is achieved. Non zero signals are reported for azimuthal asymmetries with respect the transverse target polarization in real-photon exclusive-electroproduction, which are related (still in a model dependent way) to the elusive quark orbital motion. Evidence is reported of the poorly known transversity function and of naive-T-odd transverse-momentum-dependent parton distribution functions related to spin-orbit effects. Evidence of spin-orbit effects in quark fragmentation is also observed, which are opposite in sign for favored and disfavored processes.

For transversely polarized nucleons the distribution of quarks in the transverse plane is transversely shifted and that shift can be described in terms of Generalized Parton Distributions (GPDs). This observation provides a 'partonic' derivation of the Ji-relation for the quark angular momentum in terms of GPDs. Wigner distributions are used to show that the difference between the Jaffe-Manohar definiton of quark orbital angular momentum and that of Ji is equal to the change of orbital angular momentum due to the final state interactions as the struck quark leaves the target in a DIS experiment.

Definitions of orbital angular momentum based on Wigner distributions are used to discuss the connection between the Ji definition of the quark orbital angular momentum and that of Jaffe and Manohar. The difference between these two definitions can be interpreted as the change in the quark orbital angular momentum as it leaves the target in a DIS experiment. The mechanism responsible for that change is similar to the mechanism that causes transverse single-spin asymmetries in semi-inclusive deep-inelastic scattering.

The investigation of the partonic degrees of freedom beyond collinear approximation (3D description) has been gained increasing interest in the last decade. The Thomas Jefferson National Laboratory, after the CEBAF upgrade to 12 GeV, will become the most complete facility for the investigation of the hadron structure in the valence region by scattering of polarized electron off various polarized nucleon targets. A compendium of the planned experiments is here presented.

Definitions of orbital angular momentum based on Wigner distributions are used to discuss the connection between the Ji definition of the quark orbital angular momentum and that of Jaffe and Manohar. The difference between these two definitions can be interpreted as the change in the quark orbital angular momentum as it leaves the target in a DIS experiment. The mechanism responsible for that change is similar to the mechanism that causes transverse single-spin asymmetries in semi-inclusive deep-inelastic scattering.

Generalized transverse-momentum dependent parton distributions (GTMDs) encode the most general parton structure of hadrons. In this contribution, which is largely based on a recent publication,¹ we focus on two twist-2 GTMDs which are denoted by F_1,4 and G_1,1 in parts of the literature. As already shown previously, both GTMDs have a close relation to orbital angular momentum of partons inside a hadron. However, recently even the mere existence of F_1,4 and G_1,1 has been doubted. We explain why this claim does not hold. We support our model-independent considerations by calculating the GTMDs in two spectator models and in perturbative QCD. For the model results we also explicitly check the relation to the orbital angular momentum of partons inside hadrons.

COMPASS collaboration has started in 2012 a five-year program of new measurements, which are outlined in the 'COMPASS-II' proposal. The two new major projects of the proposal are measurements of polarized Drell-Yan process in π^- scattering off transversely polarized protons and studies of GPDs via measurements of Deeply Virtual Compton Scattering and Hard Exclusive Meson Production in muon scattering off a liquid hydrogen target. In addition, high statistics SIDSI measurements with muon beams and a study of charged pion and kaon polarizabilities via Primakoff reactions with hadron beams are also foreseen as a part of this program.

Deeply virtual Compton scattering process was studied widely at the HERMES experiment through measurements of various cross-section asymmetries. These measurements exploited the rich data collected at HERMES on scattering a longitudinally polarized lepton (electron/positron) beam off unpolarized, longitudinally and transversely polarized hydrogen targets, unpolarized and longitudinally polarized deuterium targets, as well as unpolarized nuclear targets. The operation of a recoil detector during the last two years of HERMES running enabled for the full kinematic reconstruction of the events of exclusively produced real photons and a clean (with a background well below the 1$\%$) measurement of the beam-helicity asymmetry. Also, first measurement of the beam-helicity asymmetry related to the associated deeply virtual Compton scattering process, where the proton is excited to a $\mathrm{\Delta }$-resonance state, was possible using the recoil detector information.

This article briefly reviews an attempt to extract the generalized parton distributions (GPDs) from meson electroproduction data and discusses their applications such as their use in calculations of other hard exclusive processes, their behavior in the transverse position space or the evaluation of the parton angular momenta.

We calculate twist-3 parton ditribution functions (PDFs) using cut and uncut diagrams. Uncut diagrams lead to a Dirac delta function term. No such term appears when cut diagrams are used. We show that a δ(x) is necessary to satisfy the Lorentz invariance relations of twist-3 PDFs, except for the Burkhardt-Cottingham sum rule in QCD.

While twist-2 GPDs allow for a determination of the distribution of partons on the transverse plane, twist-3 GPDs contain quark-gluon correlations that provide information about the average transverse color Lorentz force acting on quarks. As an example, we use the nonforward generalization of g_T (x), to illustrate how twist-3 GPDs can provide transverse position information about that force.

Generalized TMDs (GTMDs) of hadrons are the most general two-parton correlation functions. The Fourier transforms of GTMDs are partonic Wigner functions. Both GTMDs and Wigner functions were only briefly mentioned in the EIC White Paper¹, but in the meantime, several interesting developments have happened in this field. In this write-up, we give a very brief overview of these objects and address the question whether they can play an important role for the EIC science case. To answer this question we discuss the presently known physics content of GTMDs and Wigner functions, as well as observables that are sensitive to these quantities.

The difference between the quark orbital angular momentum (OAM) defined in light-cone gauge (Jaffe-Manohar) compared to defined using a local manifestly gauge invariant operator (Ji) is interpreted in terms of the change in quark OAM as the quark leaves the target in a DIS experiment. We also discuss the possibility to measure quark OAM directly using twist 3 GPDs, and to calculate quark OAM in lattice QCD.

The Generalized Parton Distributions (GPDs) constitute an appropriate framework for a universal description of the partonic structure of the nucleon. Double Deeply Virtual Compton Scattering (DDVCS) process provides the only experimental way to measure independently the dependences of the GPDs on the average and transferred momentum. This proceeding discusses the feasibility of a DDVCS experiment in the context of JLab 12 GeV, model-predicted pseudo-data, and extraction of the relevant GPDs information based on a fitter algorithm.

We employ an effective Hamiltonian that includes the transverse and longitudinal confinement and the one-gluon exchange interaction with fixed coupling constant. By solving the eigenvalue equation in basis light-front quantization (BLFQ), we generate the light-front wavefunctions (LFWFs) for the nucleon in the valence quark Fock space. Fitting the model parameters, we obtain high quality descriptions of electromagnetic form factors and radius for proton while the results deviate somewhat from experimental data for neutron.

The QCD analysis of the recent experimental data (L3@LEP) of the hard exclusive ρρ production in two photon collisions shows that these data can be understood as a signal for the existence of an exotic isotensor resonance with a mass around 1.5 GeV. We also argue that hard exclusive reactions are a powerful tool for an experimental study of exotic hybrid mesons with J^PC = 1^-+.

An overview is given about the capabilities provided by the JLab 12 GeV Upgrade to measure deeply virtual exclusive processes with high statistics and covering a large kinematics range in the parameters that are needed to allow reconstruction of a spatial image of the nucleon's quark structure. The measurements planned with CLAS12 will cross section asymmetries with polarized beams and with longitudinally and transversely polarized proton targets in the constrained kinematics x = ±ξ. In addition, unpolarized DVCS cross sections, and doubly polarized beam target asymmetries will be measured as well. In this talk only the beam and target asymmetries will be discussed.

Lattice QCD calculations of hadron structure have seen impressive progress over the last years. In this contribution, we illustrate the recent achievements by presenting the latest lattice computation of moments of generalized parton distributions, and then focus on the impact of these results on the decomposition of the nucleon spin 1/2 in terms of quark spin and orbital angular momentum contributions. Potential discrepancies with expectations from theoretical analyses and model studies, as well as a comparison with previous lattice and phenomenological results, will be discussed in some detail.