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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.