Generalized parton distributions

We discuss how generalized parton distributions (GPDs) enter in a variety of hard exclusive processes such as deeply virtual Compton scattering (DVCS) and hard meson electroproduction reactions on the nucleon. We show some key observables which are sensitive to the various hadron structure aspects of the GPDs, and discuss their experimental status.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.60.Fz Elastic and Compton scattering - 13.60.Le Meson production - 12.38.Bx Perturbative calculations     

Generalized parton distributions with helicity flip

We show that for both quarks and gluons there are eight generalized parton distributions in the proton: four which conserve parton helicity and four which do not. We explain why time reversal invariance does not reduce this number from eight to six, as previously assumed in the literature. Received: 7 February 2001 / Published online: 23 March 2001     

Generalized parton distributions from lattice QCD

We perform a quenched lattice calculation of the first moment of twist-two generalized parton distribution functions of the proton, and assess the total quark (spin and orbital angular momentum) contribution to the spin of the proton.     

Generalized parton distributions from meson leptoproduction

Generalized parton distributions (GPDs) extracted from exclusive meson leptoproduction within the handbag approach are briefly reviewed. Only the GPD E is discussed in some detail. Applications of these GPDs to virtual Compton scattering (DVCS) and to Ji’s sum rule are also presented.     

Generalized parton distributions of the photon

We present a first calculation of the generalized parton distributions of the photon (both polarized and unpolarized) using overlaps of light-front wave functions at leading order in α and zeroth order in αs; for non-zero transverse momentum transfer and zero skewness. We present the novel parton content of the photon in transverse position space.     

Generalized parton distributions in the deuteron

We introduce generalized quark and gluon distributions in the deuteron, which can be measured in exclusive processes like deeply virtual Compton scattering and meson electroproduction. We discuss the basic properties of these distributions and point out how they probe the interplay of nucleon and parton degrees of freedom in the deuteron wave function.     

Generalized parton distributions in impact parameter space

The kinematical factor in the positivity bound (36) is incorrect. The bound correctly reads Our corrected result agrees with inequality (25) in [1], taking into account the different normalization conventions here and there.Published online: 9 October 2003Erratum published online: 10 October 2003     

Generalized parton distributions in impact parameter space

We study generalized parton distributions in the impact parameter representation, including the case of nonzero skewness . Using Lorentz invariance, and expressing parton distributions in terms of impact parameter dependent wave functions, we investigate in which way they simultaneously describe longitudinal and transverse structure of a fast moving hadron. We compare this information with the one in elastic form factors, in ordinary and in k_T-dependent parton distributions. Received: 29 May 2002 / Published online: 9 August 2002     

Generalized parton distributions from nucleon form factor data

We present a simple empirical parameterization of the x- and t-dependence of generalized parton distributions at zero skewness, using forward parton distributions as input. A fit to experimental data for the Dirac, Pauli and axial form factors of the nucleon allows us to discuss quantitatively the interplay between longitudinal and transverse partonic degrees of freedom in the nucleon (nucleon tomography). In particular we obtain the transverse distribution of valence quarks at given momentum fraction x. We calculate various moments of the distributions, including the form factors that appear in the handbag approximation to wide-angle Compton scattering. This allows us to estimate the minimal momentum transfer required for reliable predictions in that approach to be around . We also evaluate the valence contributions to the energy-momentum form factors entering Jis sum rule.Received: 16 September 2004, Revised: 15 October 2004, Published online: 17 December 2004     

Generalized parton distributions of the photon for nonzero skewness

We present a calculation of the generalized parton distributions of the photon when there is nonzero momentum transfer both in the transverse and longitudinal directions. We consider only the contributions when the photon helicity is not flipped and calculate those at leading order in electromagnetic coupling α and zeroth order in the strong coupling αs. We keep the leading logarithmic terms as well as the quark mass terms in the vertex. By taking Fourier transforms of the GPDs with respect to the transverse and longitudinal momentum transfer, we obtain the parton distributions of the photon in position space.     

Generalized parton distributions from hadronic observables: non-zero skewness

We propose a physically motivated parameterization for the unpolarized generalized parton distributions, H and E, valid at both zero and non-zero values of the skewness variable, ζ. Our approach follows a previous detailed study of the ζ=0 case where H and E were determined using constraints from simultaneous fits of the experimental data on both the nucleon elastic form factors and the deep inelastic structure functions in the non-singlet sector. Additional constraints at ζ≠0 are provided by lattice calculations of the higher moments of generalized parton distributions. We illustrate a method for extracting generalized parton distributions from lattice moments based on a reconstruction using sets of orthogonal polynomials. The inclusion in our fit of data on Deeply Virtual Compton Scattering is also discussed. Our method provides a step towards an extraction of generalized distributions based on a global fit of the available data within the given set of constraints.     

Generalized parton distributions of the pion in a Bethe-Salpeter approach

We calculate generalized parton distribution functions in a field theoretic formalism using a covariant Bethe-Salpeter approach for the determination of the bound-state wave function. We describe the procedure in an exact calculation in scalar Electrodynamics proving that the relevant corrections outside our scheme vanish. We extend the formalism to the Nambu-Jona-Lasinio model, a realistic theory of the pion. We go in both cases beyond all previous calculations and discover that all important features required by general physical considerations, like symmetry properties, sum rules and the polynomiality condition, are explicitly verified. We perform a numerical study of their behavior in the weak- and strong-coupling limits.Received: 12 May 2003, Revised: 25 November 2003, Published online: 8 June 2004PACS: 24.10.Jv Relativistic models - 11.10.St Bound and unstable states; Bethe-Salpeter equations - 13.40.Gp Electromagnetic form factors - 13.60.Fz Elastic and Compton scatteringL. Theußl: Present address: TRIUMF, Vancouver, B.C. V6T 2A3, Canada;     

Generalized parton distributions for the nucleon in chiral perturbation theory

We complete the analysis of twist-two generalized parton distributions of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. Extending our previous study of the chiral-even isosinglet sector, we give results for chiral-even isotriplet distributions and for the chiral-odd sector. We also calculate the one-loop corrections for the chiral-odd generalized parton distributions of the pion.     

Pionic parton distributions

The gluon and sea distributions of the pion are uniquely determined by the requirement of avalence-like structure of the input parton distributions at some low resolution scale. These (dynamical) results are obtained with practically no free parameters, just using the experimentally determined pionic valence distribution combined with the constraints for the pionic gluon distribution provided by direct-γ data. Simple parametrizations of the resulting parton distributions are presented in the range 10^?5?x<1 and 0.3?Q ²?10⁸ GeV² as obtained from the leading-and higher-order evolution equations.     

Demystifying generalized parton distributions

In this paper, I will explain in as simple and intuitive physical terms as possible what generalized parton distributions are, what new information about the structure of hadrons they convey and therefore what picture of the hadron will emerge. To develop this picture, I will use the example of deeply virtual Compton scattering (DVCS) and exclusive meson electroproduction processes. Based on this picture, I will then make some general predictions for these processes.Received: 2 December 2002, Revised: 20 August 2003, Published online: 2 October 2003     

Dynamical parton distributions revisited

Dynamical parton densities, generated radiatively from valence-like inputs at some low resolution scale, are confronted with recent small-x data on deep inelastic and other hard scattering processes. It is shown that within theoretical uncertainties our previous (1994) dynamical/radiative parton distributions are compatible with most recent data and still applicable within the restricted accuracy margins of the presently available next-to-leading order calculations. Due to recent high precision measurements we also present an updated, more accurate, version of our (valence-like) dynamical input distributions. Furthermore, our perturbatively stable parameter-free dynamical predictions are extended to the extremely small-x region, , relevant to questions concerning ultra-high-energy cosmic ray and neutrino astronomy. Received: 22 June 1998 / Published online: 21 August 1998     

Generalized parton distributions and deeply virtual Compton scattering in color glass condensate model

Within the framework of the color glass condensate model, we evaluate quark and gluon generalized parton distributions (GPDs) and the cross section of deeply virtual Compton scattering (DVCS) in the small-x_B region. We demonstrate that the DVCS cross section becomes independent of energy in the limit of very small x_B, which clearly indicates saturation of the DVCS cross section. Our predictions for the GPDs and the DVCS cross section at high energies can be tested at the future Electron–Ion Collider and in ultra-peripheral nucleus–nucleus collisions at the LHC. PACS  12.38.Mh; 13.60.Fz; 13.85.Fb; 24.85.+p; 25.20.Dc