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A. V. Radyushkin

Publications and source records attributed to A. V. Radyushkin.

At least 55 records · Page 3Linked to original sources
arXiv1998

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,α;t), F(x,y;t) and skewed (off&nonforward) parton distributions (SPDs) H(x,ξ;t), F_ζ(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 ζ(ξ) 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 ζor ξ. 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-ζ,X] (or [x - ξ, x + ξ]).

hep-ph↗
arXiv1998

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.

hep-ph↗
arXiv1998

QCD sum rules and soft-hard interplay for hadronic form factors

We discuss two types of contributions to hadronic form factors in QCD: hard gluon exchange and soft wave function overlap. Within the QCD sum rule approach, the hard contribution has strong numeric suppression by factor (α_s/π) ~ 0.1 for each exchange. For this reason, the soft contribution dominates at accessible momentum transfers. The ``humpy'' distribution amplitudes used to enhance hard terms cannot be derived from QCD sum rules in a self-consistent way. The estimates of soft terms obtained within the local quark-hadronic duality approach in all cases are close to existing data, providing an experimental evidence that hard terms are small.

hep-ph↗
arXiv1998

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 < p'| O(0,z) | p > of quark and gluon light-cone operators. In our previous papers we used two types of nonperturbative functions parametrizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions F_ζ(X;t). Here we discuss in more detail the double distributions (DD's) and evolution equations which they satisfy. We propose simple models for F(x,y;t=0) DD's with correct spectral and symmetry properties which also satisfy the reduction relations connecting them to the usual parton densities f(x). In this way, we obtain self-consistent models for the ζ-dependence of nonforward distributions. We show that, for small ζ, one can easily obtain nonforward distributions (in the X > ζregion) from the parton densities: F_ζ(X;t=0) \approx f(X-ζ/2).

hep-ph↗
arXiv1998

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

We argue that at moderately large momentum transfer -t <10 GeV^2, hadronic form factors and wide-angle Compton scattering amplitudes are dominated by mechanism corresponding to overlap of soft wave functions. We show that the soft contribution in both cases can be described in terms of the same universal nonforward parton densities (ND's) F(x;t), which are the simplest hybrids of the usual parton densities and hadronic form factors. We propose a simple model for ND's possessing required reduction properties. Our model easily reproduces the observed magnitude and the dipole t-dependence of the proton form factor F_1^p(t) in the region 1 GeV^2 < -t < 10 GeV^2. Our 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.

hep-ph↗
arXiv1997

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. We describe two types of nonperturbative functions parametrizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions F_ζ(X;t), discuss their spectral properties, evolution equations which they satisfy, basic uses and general aspects of factorization for hard exclusive processes.

hep-ph↗
arXiv1997

QCD sum rules: form factors and wave functions

The shape of hadronic distribution amplitudes (DAs) is a critical issue for the perturbative QCD of hard exclusive processes. Recent CLEO data on gamma gamma* -> pi^0 form factor clearly favor a pion DA close to the asymptotic form. We argue that QCD sum rules for the moments of the pion DA φ_π(x) are unreliable, so that the humpy shape of φ_π(x) obtained by Chernyak and Zhitnitsky is a result of model assumptions rather than an unambigous consequence of QCD sum rules. This conclusion is also supported by a direct QCD sum rule calculation of the gamma gamma* -> pi^0 form factor which gives a result very close to the CLEO data.

hep-ph↗
arXiv1997

The asymptotics of the transition form factor γγ* -> pi^o and QCD sum rules

In this paper we present the result of a direct QCD sum rule calculation of the transition form factor γγ* -> pi^o in the region of moderately large invariant momentum Q^2 > 1GeV^2 of the virtual photon. In contrast to pQCD, we make no assumptions about the shape of the pion distribution amplitude ϕ_π(x). Our results agree with the Brodsky-Lepage proposal that the Q^2-dependence of this form factor is given by an interpolation between its Q^2=0 value fixed by the axial anomaly and 1/Q^2 pQCD behaviour for large Q^2, with normalization corresponding to the asymptotic form ϕ_π^as (x)=6 f_πx (1-x) of the pion distribution amplitude. Our prediction for the from factor $F_{γ^*γ^*π^\circ}(q_1^2 = 0,q_2^2 = -Q^2)$ is in good agreement with new CLEO data.

hep-ph↗
arXiv1997

Transverse Momentum and Sudakov Effects in Exclusive QCD Processes: gamma* gamma pi0 Form Factor

We analyze effects due to transverse degrees of freedom in QCD calculations of the fundamental hard exclusive amplitude of $γ^*γ\to π^0$ transition. A detailed discussion is given of the relation between the modified factorization approach (MFA) of Sterman et al. and standard factorization (SFA). Working in Feynman gauge, we construct basic building blocks of MFA from the one-loop coefficient function of the SFA, demonstrating that Sudakov effects are distinctly different from higher-twist corrections. We show also that the handbag-type diagram, contrary to naive expectations, does not contain an infinite chain of $(M^2/Q^2)^n$ corrections: they come only from diagrams with transverse gluons emitted from the hard propagator. A simpler picture emerges within the QCD sum rule approach: the sum over soft $\bar q G ... G q$ Fock components is dual to $\bar qq$ states generated by the local axial current. We combine the results based on QCD sum rules with pQCD radiative corrections and observe that the gap between our curves for the asymptotic and CZ distribution amplitudes is sufficiently large for an experimental discrimination between them.

hep-ph↗
arXiv1996

Asymmetric Gluon Distributions and Hard Diffractive Electroproduction

The ``asymmetric'' matrix element that appears in the pQCD description of hard diffractive electroproduction does not coincide with that defining the gluon distribution function f_g(x). I outline a pQCD formalism based on a concept of the double distribution F_g(x,y), which specifies the fractions xp, yr, (1-y)r of the initial proton momentum p and the momentum transfer r, resp., carried by the gluons. For $t \equiv r^2 =0$, r is proportional to p: $r = ζp$, and it is convenient to parameterize the matrix element by an asymmetric distribution function ${\cal F}_ζ^g (X)$ depending on the total fractions $X \equiv x+y ζ$ and $X-ζ= x- (1-y) ζ$ of the initial hadron momentum p carried by the gluons.I formulate evolution equations for ${\cal F}_ζ^g (X)$, study some of their general properties and discuss the relationship between ${\cal F}_ζ^g (X)$, F_g(x,y) and f_g(x).

hep-ph↗
arXiv1996

Interaction of small size wave packet with hadron target

We calculate in QCD the cross section for the scattering of an energetic small-size wave packet off a hadron target. We use our results to study the small-$σ$ behaviour of $P_π(σ)$, the distribution over cross section for the pion, in the leading $α_{s}$-order.

hep-ph↗
arXiv1996

QCD Sum Rules and Virtual Compton Scattering

In this talk I report on recent progress in a few areas closely related to the virtual Compton scattering studies. In particular, I discuss the quark-hadron duality estimate of the $γ^* p \to Δ^+$ transition, QCD sum rule calculation of the $γγ^* \to π^0$ form factor, and application of perturbative QCD to deeply virtual Compton scattering at small $t$.

hep-ph↗
arXiv1996

Scaling Limit of Deeply Virtual Compton Scattering

I outline a perturbative QCD approach to the analysis of the deeply virtual Compton scattering process $γ^* p \to γp'$ in the limit of vanishing momentum transfer $t= (p' - p)^2$. The DVCS amplitude in this limit exhibits a scaling behaviour described by a two-argument distributions $F(x,y)$ which specify the fractions of the initial momentum $p$ and the momentum transfer $r \equiv p'-p$ carried by the constituents of the nucleon.The kernel $R(x,y;ξ,η)$ governing the evolution of the non-forward distributions $F(x,y)$ has a remarkable property: it produces the GLAPD evolution kernel $P(x/ξ)$ when integrated over $y$ and reduces to the Brodsky-Lepage evolution kernel $V(y,η)$ after the $x$-integration. This property is used to construct the solution of the one-loop evolution equation for the flavour non-singlet part of the non-forward quark distribution.

hep-ph↗
arXiv1996

Transition Form Factor gamma gamma* -> pi0 and QCD sum rules

The transition gamma*(q_1)gamma*(q_2) -> \pi0(p) is studied within the QCD sum rule framework. As a first step, we analyze the kinematic situation when both photon virtualities are spacelike and large. We construct a QCD sum rule for F(q_1^2,q_2^2) and show that, in the asymptotic limit |q_1^2|, |q_2^2| \to \infty, it reproduces the leading-order pQCD result. Then we study the limit |q_1^2| -> 0, in which one of the photons is (almost) real. We develop a factorization procedure for the infrared singularities ln(q_1^2), 1/q_1^2,1/q_1^4,etc., emerging in this limit. The infrared-sensitive contributions are absorbed in this approach by bilocal correlators, which can be also interpreted as the distribution amplitudes for (almost) real photon. Under explicitly formulated assumptions concerning the form of these amplitudes, we obtain a QCD sum rule for F(q_1^2=0,q_2^2=-Q^2) and study its Q^2-dependence. In contrast to pQCD, we make no assumptions about the shape of the pion distribution amplitude varphi_π(x). Our results agree with the Brodsky-Lepage proposal that the Q^2-dependence of this form factor is given by an interpolation between its Q^2=0 value fixed by the axial anomaly and 1/Q^2 pQCD value dictated by the asymptotic form of the pion distribution amplitude. We interpret this as an evidence that the latter is rather close to the asymptotic form.

hep-ph↗
arXiv1995

Quark-Hadron Duality and Intrinsic Transverse Momentum

It is demonstrated in several exclusive processes involving the pion that a local quark-hadron duality prescription is equivalent to using an effective $ \bar q q $ (two-body) light-cone wave function $Ψ^{(LD)}(x,k_{\perp})$ for the pion. This wave function models soft dynamics of all higher $\bar qG \ldots G q $ Fock components of the standard light-cone approach. Contributions corresponding to higher Fock components in a hard regime appear in this approach as radiative corrections and are suppressed by powers of $α_s/π$.

hep-ph↗
arXiv1995

QCD Sum Rule Calculation of $γγ^*\toπ^0$ Transition Form Factor

We develop a QCD sum rule analysis of the form factor $F_{γ^*γ^*π^0}(q^2,Q^2)$ in the region where virtuality of one of the spacelike photons is small $q^2 \ll 1 GeV^2$ while another is large: $Q^2 \gapprox 1 GeV^2$. We construct the operator product expansion suitable for this kinematic situation and obtain a QCD sum rule for $F_{γ^*γ^*π^0}(0,Q^2)$. Our results confirm expectation that the momentum transfer dependence of $F_{γ^*γ^*π^0}(0,Q^2)$ is close to interpolation between its $Q^2=0$ value fixed by the axial anomaly and $Q^{-2}$ pQCD behaviour for large $Q^2$. Our approach, in contrast to pQCD, does not require additional assumptions about the shape of the pion distribution amplitude $φ_π(x)$. The absolute value of the $1/Q^2$ term obtained in this paper favours $φ_π(x)$ close to the asymptotic form $φ_π^{as} (x)=6 f_π x (1-x)$.

hep-ph↗
arXiv1995

Soft Contribution to Form Factors of $γ^* p \to Δ^+$ Transition

The purely nonperturbative soft contribution to the $γ^* p \to Δ^+$ transition form factors is estimated using the local quark-hadron duality approach. Our results show that the soft contribution is dominated by the magnetic transition: the ratio $G_E^*(Q^2)/G_M^*(Q^2)$ is small for all accessible $Q^2$, in contrast to pQCD expectations that $G_E^*(Q^2) \to -G_M^*(Q^2)$. We also found that the soft contribution to the magnetic form factor is large enough to explain the magnitude of existing experimental data.

hep-ph↗