Anatoly Radyushkin

Nonforward parton distributions

Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in nonforward matrix elements of quark and gluon light-cone operators. They describe two types of nonperturbative functions parameterizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions F{_}/zeta (X;t), discuss their spectral properties, evolution equations which they satisfy, basic uses and general aspects of factorization for hard exclusive processes.

Unraveling hadron structure with generalized parton distributions

Abstract The generalized parton distributions, introduced nearly a decade ago, have emerged as a universal tool to describe hadrons in terms of quark and gluonic degrees of freedom. They combine the features of form factors, parton densities and distribution amplitudes—the functions used for a long time in studies of hadronic structure. Generalized parton distributions are analogous to the phase-space Wigner quasi-probability function of nonrelativistic quantum mechanics which encodes full information on a quantum-mechanical system. We give an extensive review of main achievements in the development of this formalism. We discuss physical interpretation and basic properties of generalized parton distributions, their modeling and QCD evolution in the leading and next-to-leading orders. We describe how these functions enter a wide class of exclusive reactions, such as electro- and photo-production of photons, lepton pairs, or mesons. The theory of these processes requires and implies full control over diverse corrections and thus we outline the progress in handling higher-order and higher-twist effects. We catalogue corresponding results and present diverse techniques for their derivations. Subsequently, we address observables that are sensitive to different characteristics of the nucleon structure in terms of generalized parton distributions. The ultimate goal of the GPD approach is to provide a three-dimensional spatial picture of the nucleon, direct measurement of the quark orbital angular momentum, and various inter- and multi-parton correlations.

Scaling limit of deeply virtual Compton scattering

The author outlines a perturbative QCD approach to the analysis of the deeply virtual Compton scattering process {gamma}{sup *}p {r_arrow} {gamma}p{prime} in the limit of vanishing momentum transfer t=(p{prime}{minus}p){sup 2}. The DVCS amplitude in this limit exhibits a scaling behavior described by a two-argument distributions F(x,y) which specify the fractions of the initial momentum p and the momentum transfer r {equivalent_to} p{prime}{minus}p carried by the constituents of the nucleon. The kernel R(x,y;{xi},{eta}) governing the evolution of the non-forward distributions F(x,y) has a remarkable property: it produces the GLAPD evolution kernel P(x/{xi}) when integrated over y and reduces to the Brodsky-Lepage evolution kernel V(y,{eta}) after the x-integration. This property is used to construct the solution of the one-loop evolution equation for the flavor non-singlet part of the non-forward quark distribution.

Nucleon form factors from generalized parton distributions

We discuss the links between Generalized Parton Distributions (GPDs) and elastic nucleon form factors. These links, in the form of sum rules, represent powerful constraints on parametrizations of GPDs. A Regge parametrization for GPDs at small momentum transfer, is extended to the large momentum transfer region and it is found to describe the basic features of proton and neutron electromagnetic form factor data. This parametrization is used to estimate the quark contribution to the nucleon spin.

Asymmetric gluon distributions and hard diffractive electroproduction

Due to the momentum transfer r{equivalent_to} p{minus}p{prime} from the initial proton to the final, the asymmetric matrix element {l_angle}p{prime}{vert_bar}G...G{vert_bar}p{r_angle} that appears in the pQCD description of hard diffractive electroproduction does not coincide with that defining the gluon distribution function f{sub g}(x). The author outlines a pQCD formalism based on a concept of the double distribution F{sub g}(x,y), which specifies the fractions xp, yr, (1{minus}y)r of the initial proton momentum p and the momentum transfer r, resp., carried by the gluons. He discusses the one-loop evolution equation for the double distribution F{sub g}(x,y,{mu}) and obtains the solution of tis equation in simplified situation when the quark-gluon mixing effects are neglected. For r{sup 2}=0, the momentum transfer r is proportional to p: r = {zeta}p, and it is convenient to parameterize the matrix element {l_angle}p{minus}r{vert_bar}G...G{vert_bar}p{r_angle} by an asymmetric distribution function F{sub {zeta}}{sup g}(X) depending on the total fractions X {equivalent_to} x+y{zeta} and X{minus}{zeta} = x{minus}(1{minus}y){zeta} of the initial hadron momentum p carried by the gluons. He formulates evolution equations for F{sub {zeta}}{sup g}(X), studies some of their general properties and discusses the relationship between F{sub {zeta}}{sup g}(X), F{sub g}(x,y) and f{sub g}(x).

Double distributions and evolution equations

Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive meson electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in nonforward matrix elements of quark and gluon light-cone operators. In their previous papers the authors used two types of nonperturbative functions parameterizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions F{sub {zeta}}(X;t). Here they discuss in more detail the double distributions (DDs) and evolution equations which they satisfy. They propose simple models for F(x,y;t=0) DDs with correct spectral and symmetry properties which also satisfy the reduction relations connecting them to the usual parton densities f(x). In this way, they obtain self-consistent models for the {zeta}-dependence of nonforward distributions. They show that, for small {zeta}, one can easily obtain nonforward distributions (in the X > {zeta} region) from the parton densities: F{sub {zeta}} (X;t=0) {approx} f(X{minus}{zeta}/2).

Nonforward parton densities and soft mechanism for form factors and wide-angle Compton scattering in QCD

The authors argue that at moderately large momentum transfer {minus}t {approx_lt} 10 GeV{sup 2}, hadronic form factors and wide-angle Compton scattering amplitudes are dominated by mechanism corresponding to overlap of soft wave functions. They show that the soft contribution in both cases can be described in terms of the same universal nonforward parton densities (NDs) F(x;t), which are the simplest hybrids of the usual parton densities and hadronic form factors. They propose a simple model for NDs possessing required reduction properties. Their model easily reproduces the observed magnitude and the dipole t-dependence of the proton form factor F{sub 1}{sup p}(t) in the region 1 GeV{sup 2} < {minus}t < 10 GeV{sup 2}. Their results for the wide-angle Compton scattering cross section follow the angular dependence of existing data and are rather close to the data in magnitude.

Sum Rules and Pion Form-Factor in QCD

Abstract We propose a new approach to the investigation of the pion electromagnetic form factor in QCD based on the systematic use of the QCD sum rule technique. The theoretical curve obtained for F π (Q 2 ) is in good agreement with existing experimental data.

Form Factors and Wave Functions of Vector Mesons in Holographic QCD

Abstract Within the framework of a holographic dual model of QCD, we develop a formalism for calculating form factors of vector mesons. We show that the holographic bound states can be described not only in terms of eigenfunctions of the equation of motion, but also in terms of conjugate wave functions that are close analogues of quantum-mechanical bound state wave functions. We derive a generalized VMD representation for form factors, and find a very specific VMD pattern, in which form factors are essentially given by contributions due to the first two bound states in the Q 2 -channel. We calculate electric radius of the ρ-meson, finding the value 〈 r ρ 2 〉 C = 0.53 fm 2 .

Structure of vector mesons in a holographic model with linear confinement

Wave functions and form factors of vector mesons are investigated in the holographic dual model of quantum chromodynamics with oscillator-like infrared cutoff. We introduce wave functions conjugate to solutions of the 5D equation of motion and develop a formalism based on these wave functions, which are very similar to those of a quantum-mechanical oscillator. For the lowest bound state (