Kinematical twist-3 effects in DVCS as a quark spin rotation

We point out that the kinematical twist-3 contributions to the DVCS amplitude, required to restore electromagnetic gauge invariance of the twist-2 amplitude up to O(t/q^2), can be understood as a spin rotation applied to the twist-2 quark density matrix in the target. This allows for a compact representation of the twist-3 effects, as well as for a simple physical interpretation.Comment: 4 pages, revtex, 3 eps figures included using eps

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: $r = \zeta p$, and it is convenient to parameterize the matrix element by an asymmetric distribution function ${\cal F}_{\zeta}^g (X)$ depending on the total fractions $X \equiv x+y \zeta$ and $X-\zeta = x- (1-y) \zeta$ of the initial hadron momentum p carried by the gluons.I formulate evolution equations for ${\cal F}_{\zeta}^g (X)$, study some of their general properties and discuss the relationship between ${\cal F}_{\zeta}^g (X)$, F_g(x,y) and f_g(x).Comment: Definition of asymmetric gluon distribution is corrected to conform with the reduction formula

A novel way to probe distribution amplitudes of neutral mesons in e^+e^- annihilation

We derive the amplitude for the process $e^+e^-\to \pi^0\pi^0$ at large invariant energy. The process goes through the two-photon exchange and its amplitude is expressed in terms of the convolution integral which depends on the shape of the pion distribution amplitude (DA) and the centre of mass scattering angle. Remarkable feature of the integral is that it is very sensitive to the end-point behaviour of the pion DA -- it starts to diverge if pion DA nullifies at the end-point as $\sqrt x$ or slower. That makes the $e^+e^-\to \pi^0\pi^0$ process unique probe of the shape of the meson DAs. The estimated cross section is rather small, for $\sqrt s = 3$ GeV it ranges from a fraction of femtobarn (for the asymptotic DA) to couple of femtobarn (for the Chernyak-Zhitnitsky DA). The observation of the process $e^+e^-\to\pi^0\pi^0$ with the cross section higher as estimated here would imply very unusual form of the pion DA, e.g. the flat one. The derived amplitude can be easily generalized to other processes like $e^+e^-\to \sigma\sigma, K_SK_S, \eta\eta, \eta^\prime\eta, \pi^0 f_2$, etc.Comment: 5 pages, 3 figure

Twist-three analysis of photon electroproduction with pion

We study twist-three effects in spin, charge, and azimuthal asymmetries in deeply virtual Compton scattering on a spin-zero target. Contributions which are power suppressed in 1/Q generate a new azimuthal angle dependence of the cross section which is not present in the leading twist results. On the other hand the leading twist terms are not modified by the twist three contributions. They may get corrected at twist four level. In the Wandzura-Wilczek approximation these new terms in the Fourier expansion with respect to the azimuthal angle are entirely determined by the twist-two skewed parton distributions. We also discuss more general issues like the general form of the angular dependence of the differential cross section, validity of factorization at twist-three level, and a relation of skewed parton distributions to spectral functions.Comment: 21 pages, LaTeX, 2 figures, text clarifications, an equation, a note and references adde

Light-Ray Evolution Equations and Leading-Twist Parton Helicity-Dependent Nonforward Distributions

We discuss the calculation of the evolution kernels \Delta W_{\zeta}(X,Z) for the leading-twist nonforward parton distributions G_\zeta(X,t) sensitive to parton helicities. We present our results for the kernels governing evolution of the relevant light-ray operators and describe a simple method allowing to obtain from them the components of the nonforward kernels \Delta W_{\zeta}(X,Z).Comment: 8 pages; final version, to appear in Physics Letters

Pedagogic model for Deeply Virtual Compton Scattering with quark-hadron duality

We show how quark-hadron duality can emerge for valence spin averaged structure functions, and for the non-forward distributions of Deeply Virtual Compton Scattering. Novel factorisations of the non-forward amplitudes are proposed. Some implications for large angle scattering and deviations from the quark counting rules are illustrated.Comment: Version accepted by Phys. Rev.

Scaling Limit of Deeply Virtual Compton Scattering

I outline a perturbative QCD approach to the analysis of the deeply virtual Compton scattering process $\gamma^* p \to \gamma p'$ 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 $R(x,y;\xi,\eta)$ 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 flavour non-singlet part of the non-forward quark distribution.Comment: gziped, tar file of LaTeX paper plus 2 postscript figures,10 pages; some changes in new terminolog

DVCS amplitude with kinematical twist-3 terms

We compute the amplitude of deeply virtual Compton scattering (DVCS) using the calculus of QCD string operators in coordinate representation. To restore the electromagnetic gauge invariance (transversality) of the twist-2 amplitude we include the operators of twist-3 which appear as total derivatives of twist-2 operators. Our results are equivalent to a Wandzura-Wilczek approximation for twist-3 skewed parton distributions. We find that this approximation gives a finite result for the amplitude of a longitudinally polarized virtual photon, while the amplitude for transverse polarization is divergent, i.e., factorization breaks down in this term. However, the divergent part has zero projection onto the polarization vector of the final real photon.Comment: 8 pages, Latex; discussion of singularities correcte

DVCS on the nucleon : study of the twist-3 effects

We estimate the size of the twist-3 effects on deeply virtual Compton scattering (DVCS) observables, in the Wandzura-Wilczek approximation. We present results in the valence region for the DVCS cross sections, charge asymmetries and single spin asymmetries, to twist-3 accuracy.Comment: 20 pages, 6 figure

Positivity bounds on generalized parton distributions in impact parameter representation

New positivity bounds are derived for generalized (off-forward) parton distributions using the impact parameter representation. These inequalities are stable under the evolution to higher normalization points. The full set of inequalities is infinite. Several particular cases are considered explicitly.Comment: 8 page