Deeply Virtual Compton Scattering: Facing Nonforward Distributions

Applications of perturbative QCD to deeply virtual Compton scattering process require a generalization of usual parton distributions for the case when long-distance information is accumulated in nonforward matrix elements of quark and gluon operators. We discuss two types of functions parametrizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions \cal F_\zeta (X;t) and also their relation to usual parton densities f(x).Comment: 4 pages, to be published in the Proceedings of the International Conference on Deep Inelastic Scattering, Chicago, April 1997, AI

Asymmetric Parton Distributions

Applications of perturbative QCD to hard exclusive electroproduction processes in the Bjorken limit at small invariant momentum transfer t bring in a new type of parton distributions which have hybrid properties, resembling both the parton distribution functions and the distribution amplitudes. Their t-dependence is analogous to that of hadronic form factors. We discuss general properties of these new parton distributions, their relation to usual parton densities and the evolution equations which they satisfy.Comment: 4 pages, to be published in the Proceedings of the International Conference on Deep Inelastic Scattering, Chicago, April 1997, AI

Generalized Parton Distributions and Pseudodistributions

We derive one-loop matching relations for the Ioffe-time distributions (ITDs) related to the pion distribution amplitude (DA) and generalized parton distributions (GPDs). They are obtained from a universal expression for the one-loop correction in an operator form, and will be used in the ongoing lattice calculations of the pion DA and GPDs within the parton pseudodistributions approach

Virtuality Distributions in Application to ɣɣ* → π\u3csup\u3e​0\u3c/sup\u3e Transition Form Factor at Handbag Level

We outline basics of a new approach to transverse momentum dependence in hard processes. As an illustration, we consider hard exclusive transition process ɣ*ɣ -\u3e π0 at the handbag level. Our starting point is coordinate representation for matrix elements of operators (in the simplest case, bilocal O(0, z)) describing a hadron with momentum p. Treated as functions of (pz) and z2, they are parametrized through virtuality distribution amplitudes (VDA) Φ(x, σ), with x being Fourier-conjugate to (pz) and σ Laplace-conjugate to z2. For intervals with z+ = 0, we introduce the transverse momentum distribution amplitude (TMDA) Ѱ(x, k┴), and write it in terms of (VDA) Φ(x, σ). The results of covariant calculations, written in terms of Φ(x, σ) are converted into expressions involving Ѱ(x, k┴) Starting with scalar toy models, we extend the analysis onto the case of spin-1/2 quarks and QCD. We propose simple models for soft VDAs/TMDAs, and use them for comparison of handbag results with experimental (BaBar and BELLE) data on the pion transition form factor. We also discuss how one can generate high-k┴ tails from primordial soft distributions

Method of Analytic Evolution of Flat Distribution Amplitudes in QCD

A new analytical method of performing ERBL evolution is described. The main goal is to develop an approach that works for distribution amplitudes that do not vanish at the end points, for which the standard method of expansion in Gegenbauer polynomials is inefficient. Two cases of the initial DA are considered: a purely flat DA, given by the same constant for all x, and an antisymmetric DA given by opposite constants for x 1/2. For a purely flat DA, the evolution is governed by an overall (x (1-x))^t dependence on the evolution parameter t times a factor that was calculated as an expansion in t. For an antisymmetric flat DA, an extra overall factor |1-2x|^{2t} appears due to a jump at x=1/2. A good convergence was observed in the t < 1/2 region. For larger t, one can use the standard method of the Gegenbauer expansion.Comment: Talk at the QCD Evolution workshop: from collinear to non collinear case. April 8-9, 2011, Jefferson Lab, Newport News, Virginia. To be published in the International Journal of Modern Physics: Conference Serie

BB-meson Ioffe-time distribution amplitude at short distances

We propose the approach for a lattice investigation of light-cone distribution amplitudes (LCDA) of heavy-light mesons, such as the $B$-meson, using the formalism of parton pseudo-distributions. A basic ingredient of the approach is the study of short-distance behavior of the $B$-meson Ioffe-time distribution amplitude (ITDA), which is a generalization of the $B$-meson LCDA in coordinate space. We construct a reduced ITDA for the $B$-meson, and derive the matching relation between the reduced ITDA and the LCDA. The reduced ITDA is ultraviolet finite, which guarantees that the continuum limit exists on the lattice.Comment: 6 pages, 1 figure, version published in Phys. Rev.

\u3cb\u3eB\u3c/b\u3e-Meson Ioffe-Time Distribution Amplitude at Short Distances

We propose the approach for a lattice investigation of light cone distribution amplitudes (LCDA) of heavy-light mesons, such as the B meson, using the formalism of parton pseudodistributions. A basic ingredient of the approach is the study of short-distance behavior of the B-meson Ioffe-time distribution amplitude (ITDA), which is a generalization of the B-meson LCDA in coordinate space. We construct a reduced ITDA for the B meson, and derive the matching relation between the reduced ITDA and the LCDA. The reduced ITDA is ultraviolet finite, which guarantees that the continuum limit exists on the lattice

Singularities of Generalized Parton Distributions

Progress of recent work on modeling generalized parton distributions is given. Special attention was paid to study of their singularities structure

Higher Fock State Contributions to the Generalized Parton Distribution of Pion

We discuss the higher Fock state (q \bar q g) contributions to the nonzero value of the pion GPD at the crossover point x = zeta between the DGLAP and ERBL regions. Using the phenomenological light-front constituent quark model, we confirm that the higher Fock state contributions indeed give a nonzero value of the GPD at the crossover point. Iterating the light-front quark model wave function of the lowest q \bar q Fock state with the Bethe-Salpeter kernel corresponding to the one-gluon-exchange, we include all possible time-ordered q \bar q g Fock state contributions and obtain the pion GPD satisfying necessary sum rules and continuity conditions.Comment: References adde