Quark phase-space distributions and orbital angular momentum

We discuss the Wigner functions of the nucleon which provide multi-dimensional images of the quark distributions in phase space. They combine in a single picture all the information contained in the generalized parton distributions (GPDs) and the transverse-momentum dependent parton distributions (TMDs). In particular, we present results for the distribution of unpolarized quarks in a longitudinally polarized nucleon obtained in a light-cone constituent quark model. We show how quark orbital angular momentum can be extracted from these distributions and compare it with alternative definitions given in terms of the GPDs and the TMDs.Comment: 5 pages, 1 figure, 1 table, prepared for the Sixth International Conference on Quarks and Nuclear Physics, April 16-20, 2012, Ecole Polytechnique, Palaiseau, Franc

Generalized Transverse-Momentum Dependent Parton Distributions in Light-Cone Quark Models

We discuss the general formalism for the calculation in light-cone quark models of the fully unintegrated, off-diagonal quark-quark correlator of the nucleon. The corresponding distributions in impact parameter space are the Wigner or phase-space distributions. The results obtained in two different light-cone quark models in the case of unpolarized quarks in an unpolarized proton are very similar and present a non-trivial shape which can be understood as due to the orbital motion of the quarks.Comment: Proceedings for the "Light Cone 2010 Relativistic Hadronic and Particle Physics" workshop, 3 Figs, 8p

Quark Wigner Distributions and Orbital Angular Momentum

We study the Wigner functions of the nucleon which provide multidimensional images of the quark distributions in phase space. These functions can be obtained through a Fourier transform in the transverse space of the generalized transverse-momentum dependent parton distributions. They depend on both the transverse position and the three-momentum of the quark relative to the nucleon, and therefore combine in a single picture all the information contained in the generalized parton distributions and the transverse-momentum dependent parton distributions. We focus the discussion on the distributions of unpolarized/longitudinally polarized quark in an unpolarized/longitudinally polarized nucleon. In this way, we can study the role of the orbital angular momentum of the quark in shaping the nucleon and its correlations with the quark and nucleon polarizations. The quark orbital angular momentum is also calculated from its phase-space average weighted with the Wigner distribution of unpolarized quarks in a longitudinally polarized nucleon. The corresponding results obtained within different light-cone quark models are compared with alternative definitions of the quark orbital angular momentum, as given in terms of generalized parton distributions and transverse-momentum dependent parton distributions.Comment: 29 pages, 10 figures, 3 table

The electron in three-dimensional momentum space

We study the electron as a system composed by an electron and a photon, using lowest order perturbation theory. We derive the leading-twist transverse-momentum-dependent distribution functions for both the electron and photon in the dressed electron, thereby offering a three-dimensional description of the dressed electron in momentum space. To obtain the distribution functions, we apply both the formalism of light-front wave function overlap representation and the diagrammatic approach. We perform the calculations both in light-cone gauge and Feynman gauge, and we present a detailed discussion of the role of the Wilson lines to obtain gauge-independent results. We provide numerical results and plots for many of the computed distributions.Comment: 25 pages, 14 figure

Spatial distribution of angular momentum inside the nucleon

We discuss in detail the spatial distribution of angular momentum inside the nucleon. We show that the discrepancies between different definitions originate from terms that integrate to zero. Even though these terms can safely be dropped at the integrated level, they have to be taken into account at the density level. Using the scalar diquark model, we illustrate our results and, for the first time, check explicitly that the equivalence between kinetic and canonical orbital angular momentum persists at the density level, as expected in a system without gauge degrees of freedom

The transverse structure of the pion in momentum space inspired by the AdS/QCD correspondence

We study the internal structure of the pion using a model inspired by the AdS/QCD correspondence. The holographic approach provides the light-front wave function (LFWF) for the leading Fock state component of the pion. We adopt two different forms for the LFWF derived from the AdS/QCD soft-wall model, with free parameters fitted to the available experimental information on the pion electromagnetic form factor and the leading-twist parton distribution function. The intrinsic scale of the model is taken as an additional fit parameter. Within this framework, we provide predictions for the unpolarized transverse momentum dependent parton distribution (TMD), and discuss its property both at the scale of the model and after TMD evolution to higher scales that are relevant for upcoming experimental measurements.Comment: 10 pages, 6 figure

Probing the parton content of the nucleon

The parton content of the nucleon is explored within a meson-cloud model developed to derive light-cone wave functions for the physical nucleon. The model is here applied to study electromagnetic form factors, distribution amplitudes and nucleon-to-meson transition distribution amplitudes.Comment: 10 pages, 6 figures; proceedings of the workshop "Recent Advances in Perturbative QCD and Hadronic Physics" in Honor of Prof. Anatoly Efremov's 75th Birthday Celebration; to appear in Mod. Phys. Lett.

Reconstructing parton densities at large fractional momenta

Parton distribution functions (PDFs) are nonperturbative objects defined by nonlocal light-cone correlations. They cannot be computed directly from Quantum Chromodynamics (QCD). Using a standard lattice QCD approach, it is possible to compute moments of PDFs, which are matrix elements of local operators. Recently, an alternative approach has been proposed, based on the introduction of quasi-parton distribution functions (quasi-PDFs), which are matrix elements of equal-time spatial correlations and hence calculable on lattice. Quasi-PDFs approach standard PDFs in the limit of very large longitudinal proton momenta $P^z$. This limit is not attainable in lattice simulations, and quasi-PDFs fail to reproduce PDFs at high fractional longitudinal momenta. In this paper, we propose a method to improve the reconstruction of PDFs by combining information from quasi-PDFs and from the Mellin moments of regular PDFs. We test our method using the diquark spectator model for up and down valence distributions of both unpolarized and helicity PDFs. In the future, the method can be used to produce PDFs entirely based on lattice QCD results.Comment: 12 pages, 7 double-panel figures in pdf, RevTeX4-

Beam normal spin asymmetry for the ep→eΔ(1232)e p \to e \Delta(1232) process

We calculate the single spin asymmetry for the $e p \to e \Delta(1232)$ process, for an electron beam polarized normal to the scattering plane. Such single spin asymmetries vanish in the one-photon exchange approximation, and are directly proportional to the absorptive part of a two-photon exchange amplitude. As the intermediate state in such two-photon exchange process is on its mass shell, the asymmetry allows one to access for the first time the on-shell $\Delta \to \Delta$ as well as $N^\ast \to \Delta$ electromagnetic transitions. We present the general formalism to describe the $e p \to e \Delta$ beam normal spin asymmetry, and provide a numerical estimate of its value using the nucleon, $\Delta(1232)$, $S_{11}(1535)$, and $D_{13}(1520)$ intermediate states. We compare our results with the first data from the Qweak@JLab experiment and give predictions for the A4@MAMI experiment.Comment: 18 pages, 9 figure

Hadron tomography through Wigner distributions

We study the Wigner functions of the nucleon which provide multidimensional images of the quark distributions in phase space and combine in a single picture all the information contained in the generalized parton distributions (GPDs) and the transverse-momentum dependent parton distributions (TMDs). In particular, we present results for the distribution of unpolarized quarks in a longitudinally polarized nucleon obtained in a light-cone constituent quark model. Treating the Wigner distribution as it was a classical distribution, we obtain the quark orbital angular momentum and compare it with alternative definitions given in terms of the GPDs and the TMDs.Comment: 6 pages, 1 figure, 1 table, Prepared for the Third International Workshop on Transverse Polarization Phenomena in Hard Scattering (Transversity2011), Veli Lo\v{s}inj, Croatia, 29 Aug - 2 Sep 201