We present a physically motivated parametrization of the chiral-even generalized parton distributions in the non-singlet sector obtained from a global analysis using a set of available experimental data. Our analysis is valid in the kinematical region of intermediate Bjorken x and for Q 2 in the multi-GeV region which is accessible at present and currently planned facilities. Relevant data included in our fit are from the nucleon elastic form factors measurements, and from deep inelastic scattering experiments. Additional information provided by lattice calculations of the higher moments of generalized parton distributions, is also considered. Recently extracted observables from Deeply Virtual Compton Scattering on the nucleon are reproduced by our fit.

We give an interpretation of the u and d quarks contributions to the nucleon electromagnetic form factors for values of the four-momentum transfer in the multi-GeV region where flavor separated data have been recently made available. The data show, in particular, a suppression of d quarks with respect to u quarks at large momentum transfer. This trend can be explained using a reggeized diquark model calculation of generalized parton distributions, thus providing a correlation between momentum and coordinate spaces, both of which are necessary in order to interpret the partonic substructure of the form factors. We extend our discussion to the second moments of generalized parton distributions which are believed to contribute to partonic angular momentum.

Our original suggestion to investigate exclusive π o 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, Q 2 , and iii) the angular momentum, parity, and charge conjugation constraints (J P C 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 distributionsthat 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 the twist three contributions associated to orbital angular momentum are related to the target-spin asymmetry in deeply virtual Compton scattering, already measured at HERMES.PACS numbers: 13.60.Hb, 13.40.Gp, 24.85.+p 1. Considerable attention has been devoted to the partons' Transverse Momentum Distributions (TMDs), to the Generalized Parton Distributions (GPDs), and to finding a connection between the two [1-3]. TMDs are distributions of different spin configurations of quarks and gluons within the nucleon whose longitudinal and transverse momenta can be accessed in Semi-Inclusive Deep Inelastic Scattering (SIDIS). GPDs are real amplitudes for quarks or gluons being probed in a hard process and then returning to reconstitute a scattered nucleon. They are accessed through exclusive electroproduction of vector bosons along with the nucleon. In each case there is a nucleon matrix element of bilinear, non-local quark or gluon field operators. In principle both TMDs and GPDs are different limits of Wigner distributions, i.e. the phase space distributions in momenta and impact parameters. The purely momentum space form of those are the Generalized TMDs (GTMDs). GTMDs correlate hadronic states with same parton longitudinal momentum, x (assuming zero skewness), different relative transverse distance, z T = b in − b out , between the struck parton's initial and final (out) states, and same average transverse distance, b = (b in + b out )/2, of the struck parton with respect to the center of momentum [4] (Figure 1a).Understanding the angular momentum or spin structure of the nucleon is a major reason for these various distri-FIG. 1: (a) Left: Correlation function for a GTMD; (b) quark-proton scattering in the u-channel.

New data from Belle and BaBar Collaborations on azimuthal asymmetries, measured in e + e − annihilations into pion pairs at Q 2 = 112 GeV 2 , allow to take the first, direct glance at the p ⊥ dependence of the Collins functions, in addition to their z dependence. These data, together with available Semi-Inclusive Deep Inelastic Scattering (SIDIS) data on the Collins asymmetry, are simultaneously analysed in the framework of the generalised parton model assuming two alternative Q 2 evolution schemes and exploiting two different parameterisations for the Collins functions. The corresponding results for the transversity distributions are presented. Analogous data, newly released by the BESIII Collaboration, on e + e − annihilations into pion pairs at the lower Q 2 of 13 GeV 2 , offer the possibility to explore the sensitivity of these azimuthal correlations on transverse momentum dependent evolution effects. PACS numbers: 13.88.+e, 13.85.Ni I. INTRODUCTIONOur knowledge of the 3-dimensional partonic structure of the nucleon in momentum space is encoded, at leadingtwist, in eight Transverse Momentum Dependent Parton Distribution Functions (TMD-PDFs). They depend on two variables, the light-cone momentum fraction, x, of the parent nucleon's momentum carried by a parton and the parton transverse momentum, k ⊥ , with respect to the direction of the nucleon's motion. At a low resolution scale Q 2 the transverse momentum k ⊥ may be associated with the intrinsic motion of confined partons inside the nucleon. For polarised nucleons and partons there is a further dependence on the spins of the nucleon and the parton. In addition, the QCD radiation of gluons induces a dependence on the scale Q 2 at which the nucleon is being explored.Similarly, the hadronisation process of a parton into the final hadron is encoded in the Transverse Momentum Dependent parton Fragmentation Functions (TMD-FFs), which, in addition to spin depend on the light-cone momentum fraction, z, of the fragmenting parton carried by the hadron and the hadron transverse momentum, p ⊥ , with respect to the parton direction. For final spinless or unpolarised hadrons there are, at leading-twist, two independent TMD-FFs.So far, among the polarised leading twist TMD-PDFs and TMD-FFs, the Sivers distribution [1, 2] and the Collins fragmentation function [3] have clearly shown their non negligible effects in several different experimental measurements. The former describes the correlation between the intrinsic momentum k ⊥ of unpolarised partons and the parent nucleon transverse spin; as such, it must be related to parton orbital angular momentum. The latter describes the correlation between the transverse spin of a fragmenting quark and the transverse momentum p ⊥ of the final produced hadron, typically a pion, with respect to the quark direction; as such, it reveals fundamental properties of the hadronization process. This paper is devoted to the study of the Collins functions.The Collins fragmentation function can be studied in Semi-Inclusive Deep Inelastic Sc...

We provide the general expression of the cross section for exclusive deeply virtual photon electroproduction from a spin 1/2 target using current parameterizations of the off-forward correlation function in a nucleon for different beam and target polarization configurations up to twist three accuracy. All contributions to the cross section including deeply virtual Compton scattering, the Bethe-Heitler process, and their interference, are described within a helicity amplitude based framework which is also relativistically covariant and readily applicable to both the laboratory frame and in a collider kinematic setting. Our formalism renders a clear physical interpretation of the various components of the cross section by making a connection with the known characteristic structure of the electron scattering coincidence reactions. In particular, we focus on the total angular momentum, Jz, and on the orbital angular momentum, Lz. On one side, we uncover an avenue to a precise extraction of Jz, given by the combination of generalized parton distributions, H + E, through a generalization of the Rosenbluth separation method used in elastic electron proton scattering. On the other, we single out for the first time, the twist three angular modulations of the cross section that are sensitive to Lz. The proposed generalized Rosenbluth technique adds constraints and can be extended to additional observables relevant to the mapping of the 3D structure of the nucleon. *

We present a phenomenological analysis of the cos ϕ and cos 2ϕ asymmetries in unpolarized semiinclusive deep inelastic scattering, based on the recent multidimensional data released by the COMPASS and HERMES collaborations. In the transverse-momentum-dependent framework, valid at relatively low transverse momenta, these asymmetries arise from intrinsic transverse momentum and transverse spin effects, and from their correlations. The role of the Cahn and Boer-Mulders effects in both azimuthal moments is explored up to order 1=Q. As the kinematics of the present experiments is dominated by the low-Q 2 region, higher-twist contributions turn out to be important, affecting the results of our fits.

We present a physically motivated parameterization of the chiral-odd generalized parton distributions. The parametrization is an extension of our previous one in the chiral-even sector which was based on the reggeized diquark model. While for chiral even generalized distributions a quantitative fit with uncertainty estimation can be performed using deep inelastic scattering data, nucleon electromagnetic, axial and pseudoscalar form factors measurements, and all available deeply virtual Compton scattering data, the chiral-odd sector is far less constrained. While awaiting the analysis of measurements on pseudoscalar mesons exclusive electroproduction which are key for the extraction of chiral odd GPDs, we worked out a connection between the chiral-even and chiral-odd reduced helicity amplitudes using Parity transformations. The connection works for a class of models including two-components models. This relation allows us to estimate the size of the various chiral odd contributions and it opens the way for future quantitative fits.