Quark Pseudo-Distributions at Short Distances

We perform a one-loop study of the small-$z_3^2$ behavior of the Ioffe-time distribution (ITD) ${\cal M} (\nu, z_3^2)$, the basic function that may be converted into parton pseudo- and quasi-distributions. We calculate the corrections at the operator level, so that our results may be later used for pseudo-distribution amplitudes and generalized parton pseudo-distributions. We separate two sources of the $z_3^2$-dependence at small $z_3^2$. One is related to the ultraviolet (UV) singularities generated by the gauge link, and another to short-distance logarithms generating perturbative evolution of parton densities. Our calculation explicitly shows that, for a finite UV cut-off, the UV-singular terms vanish when $z_3^2=0$. The UV divergences are absent in the ratio ${\cal M} (\nu, z_3^2)/{\cal M} (0, z_3^2)$ ("reduced" ITD). Still, it has a non-trivial short-distance behavior due to $\ln z_3^2 \Lambda^2$ terms generating perturbative evolution of the parton densities. We give an explicit expression, up to constant terms, for the reduced ITD at one loop. It may be used in extraction of PDFs from the lattice QCD simulations. We also use our results to get new insights concerning the structure of parton quasi-distributions at one-loop level.Comment: 10 pages, 4 figures, typos fixed, references added, some changes in tex

Symmetries and structure of skewed and double distributions

Extending the concept of parton densities onto nonforward matrix elements of quark and gluon light-cone operators, one can use two types of nonperturbative functions: double distributions (DDs) f(x,\alpha;t), F(x,y;t) and skewed (off&nonforward) parton distributions (SPDs) H(x,\xi;t), F_\zeta(X,t). We treat DDs as primary objects producing SPDs after integration. We emphasize the role of DDs in understanding interplay between X (x) and \zeta (\xi) dependences of SPDs.In particular, the use of DDs is crucial to secure the polynomiality condition: Nth moments of SPDs are Nth degree polynomials in the relevant skewedness parameter \zeta or \xi. We propose simple ansaetze for DDs having correct spectral and symmetry properties and derive model expressions for SPDs satisfying all known constraints. Finally, we argue that for small skewedness, one can obtain SPDs from the usual parton densities by averaging the latter with an appropriate weight over the region [X-\zeta,X] (or [x - \xi, x + \xi]).Comment: 10 pages, Latex, 3 figure

Compton scattering and nonforward parton distributions

The hard exclusive electroproduction processes provide new information about hadronic structure accumulated in nonforward parton distributions. The NFPD's are universal hybrid functions having the properties of parton densities, hadronic form factors and distribution amplitudes. They give a unified description of various hard exclusive and inclusive reactions. The basic supplier of information about nonforward parton distributions is deeply virtual Compton scattering which offers a remarkable example of Bjorken scaling phenomena in exclusive processes. Wide-angle real Compton scattering is an ideal tool to test angle-dependent scaling laws characteristic for soft overlap mechanism. Hard meson electroproduction is the best candidate to see pQCD hard gluon exchange in exclusive reactions.Comment: 11 pages, Latex, 6 figures; Contribution to proceedings of the workshop ``Physics and instrumentation with 6-12 GeV beams'', Jefferson Lab, June 15-18, 199

Modeling Nucleon Generalized Parton Distributions

We discuss building models for nucleon generalized parton distributions (GPDs) H and E that are based on the formalism of double distributions (DDs). We found that the usual "DD+D-term" construction should be amended by an extra term, \xi E^1_+(x,\xi) built from the \alpha/\beta moment of the DD e(\beta,\alpha) that generates GPD E(x,\xi). Unlike the D-term, this function has support in the whole -1 \leq x \leq 1 region, and in general does not vanish at the border points |x|=\xi.Comment: Minor fixes, version to be published in PR