DVCS Amplitude Research Articles

Analyticity and sum rules for photon GPDs

The photon is explored as an object to test the applications of QCD to the perturbatively calculable collinear parton distributions. We investigate analytic properties of DVCS amplitudes and related sum rules of generalized parton distributions of the photon using as an input their earlier calculations in the leading order. The relation of these GPDs to the quintessential functions in the framework of the dual parametrization approach is also found.

Dual parametrization and Abel transform tomography for twist-3 DVCS

We derive the dual parametrization for the DVCS amplitude to the twist-3 accuracy. The relation of the dual parametrization to the Abel transform tomography for amplitudes of hard exclusive processes is elaborated. We prove the dispersion relations for the twist-3 DVCS amplitude in the Wandzura–Wilczek approximation and show that the subtraction constant is given by the D-term form factor.

Timelike virtual compton scattering from electron-positron radiative annihilation

We propose measurements of the deeply virtual Compton amplitude (DVCS), gamma* to H H-bar gamma, in the timelike t = (p_{H} + p_{H-bar})^2 > 0 kinematic domain which is accessible at electron-positron colliders via the radiative annihilation process e+ e- to H H-bar gamma. These processes allow the measurement of timelike deeply virtual Compton scattering for a variety of H H-bar hadron pairs such as pi+ pi-, K+ K-, and D D-bar as well as p p-bar. As in the conventional spacelike DVCS, there are interfering coherent amplitudes contributing to the timelike processes involving C= - form factors. The interference between the amplitudes measures the phase of the C=+ timelike DVCS amplitude relative to the phase of the timelike form factors and can be isolated by considering the forward-backward e+ \leftrightarrow e- asymmetry. The J=0 fixed pole contribution which arises from the local coupling of the two photons to the quark current plays a special role. As an example we present a simple model.

Dual parametrization of GPDs versus the double distribution Ansatz

We establish a link between the dual parametrization of GPDs and a popular parametrization based on the double distribution Ansatz, which is in prevalent use in phenomenological applications. We compute several first forward-like functions that express the double distribution Ansatz for GPDs in the framework of the dual parametrization and show that these forward-like functions make the dominant contribution into the GPD quintessence function. We also argue that the forward-like functions $Q_{2 \nu}(x)$ with $\nu \ge 1$ contribute to the leading singular small-$x_{Bj}$ behavior of the imaginary part of DVCS amplitude. This makes the small-$x_{Bj}$ behavior of $\im A^{DVCS}$ independent of the asymptotic behavior of PDFs. Assuming analyticity of Mellin moments of GPDs in the Mellin space we are able to fix the value of the $D$-form factor in terms of the GPD quintessence function $N(x,t)$ and the forward-like function $Q_0(x,t)$.

Hadron optics in three-dimensional invariant coordinate space from deeply virtual Compton scattering

The Fourier transform of the deeply virtual Compton scattering amplitude (DVCS) with respect to the skewness parameter $\ensuremath{\zeta}={Q}^{2}/2p\ifmmode\cdot\else\textperiodcentered\fi{}q$ can be used to provide an image of the target hadron in the boost-invariant variable $\ensuremath{\sigma}$, the coordinate conjugate to light-front time $\ensuremath{\tau}=t+z/c$. As an illustration, we construct a consistent covariant model of the DVCS amplitude and its associated generalized parton distributions using the quantum fluctuations of a fermion state at one loop in QED, thus providing a representation of the light-front wave functions (LFWFs) of a lepton in $\ensuremath{\sigma}$ space. A consistent model for hadronic amplitudes can then be obtained by differentiating the light-front wave functions with respect to the bound-state mass. The resulting DVCS helicity amplitudes are evaluated as a function of $\ensuremath{\sigma}$ and the impact parameter ${\stackrel{\ensuremath{\rightarrow}}{b}}_{\ensuremath{\perp}}$, thus providing a light-front image of the target hadron in a frame-independent three-dimensional light-front coordinate space. Models for the LFWFs of hadrons in $(3+1)$ dimensions displaying confinement at large distances and conformal symmetry at short distances have been obtained using the AdS/CFT method. We also compute the LFWFs in this model in invariant three-dimensional coordinate space. We find that, in the models studied, the Fourier transform of the DVCS amplitudes exhibit diffraction patterns. The results are analogous to the diffractive scattering of a wave in optics where the distribution in $\ensuremath{\sigma}$ measures the physical size of the scattering center in a one-dimensional system.

Nuclear effects and their interplay in nuclear deeply virtual Compton scattering amplitudes

In this paper we analyze nuclear medium effects on DVCS amplitudes in the $\Bx$ range of $0.1-0.0001$ for a large range of $Q^2$ and four different nuclei. We use our nucleon GPD model capable of describing all currently available DVCS data on the proton and extend it to the nuclear case using two competing parameterizations of nuclear effects. The two parameterizations, though giving different absolute numbers, yield the same type and magnitude of effects for the imaginary and real part of the nuclear DVCS amplitude. The imaginary part shows stronger nuclear shadowing effects compared to the inclusive case i.e. $F^N_2$, whereas in the real part nuclear shadowing at small $\Bx$ and anti-shadowing at large $\Bx$ combine through evolution to yield an even greater suppression than in the imaginary part up to large values of $\Bx$. This is the first time that such a combination of nuclear effects has been observed in a hadronic amplitude. The experimental implications will be discussed in a subsequent publication.

Theory of deeply virtual Compton scattering on the nucleon

We compute the cross section for leptoproduction of the real photon off the nucleon, which is sensitive to the deeply virtual Compton scattering amplitude with power accuracy. Our considerations go beyond the leading twist and involve the complete analysis in the twist-three approximation. We discuss consequences of the target and lepton beam polarizations for accessing the generalized parton distributions from experimental measurements of the azimuthal angular dependence of the final state photon or nucleon. We introduce several sets of asymmetries, defined as Fourier moments with respect to the azimuthal angle, which allow for a clear separation of the twist-two and -three sectors. Relying on a simple ansatz for the generalized parton distributions, we give quantitative estimates for azimuthal and spin asymmetries, discuss the uncertainties of these predictions brought in by radiative corrections, and compare them with experimental data as well as other theoretical expectations. Furthermore, we derive a general parametrization of the DVCS amplitudes in the region of small Bjorken variable.

Observation of Exclusive Deeply Virtual Compton Scattering in Polarized Electron Beam Asymmetry Measurements

We report the first results of the beam spin asymmetry measured in the reaction e + p -> e + p + gamma at a beam energy of 4.25 GeV. A large asymmetry with a sin(phi) modulation is observed, as predicted for the interference term of Deeply Virtual Compton Scattering and the Bethe-Heitler process. The amplitude of this modulation is alpha = 0.202 +/- 0.028. In leading-order and leading-twist pQCD, the alpha is directly proportional to the imaginary part of the DVCS amplitude.

Kinematical twist-3 effects in deeply virtual Compton scattering 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.

Wandzura–Wilczek approximation for the twist-3 DVCS amplitude

We present a derivation of Wandzura–Wilczek (WW) like relations for skewed parton distributions. It is demonstrated for photon-pion scattering that the skewed twist-3 parton distributions contributing to the DVCS amplitude have discontinuities at the points x=± ξ in the WW approximation. This may lead to a violation of factorisation for the twist-3 DVCS amplitude with transverse polarization of the virtual photon. We show, however, that the contribution of the divergencies to the scattering of a transversely polarized virtual photon affects DVCS observables only at order 1/ Q 2 and can be neglected at twist-3 accuracy. For the scattering of a longitudinally polarized photon the twist-3 amplitude is free of such divergencies.

Deeply virtual Compton scattering amplitude in the parton model

We compute amplitude of deeply virtual Compton scattering in the parton model. We found that the amplitude up to the accuracy O(1/ Q) depends on new skewed parton distributions (SPDs). These additional contributions make the DVCS amplitude explicitly transverse.

Erratum: Diffractive exclusive photon production in DIS at DESY HERA [Phys. Rev. D58, 114001 (1998)

We demonstrate that perturbative QCD allows one to calculate the absolute cross section of diffractive exclusive production of photons at large $Q^2$ at HERA, while the aligned jet model allows one to estimate the cross section for intermediate $Q^2 \sim 2 GeV^2$. Furthermore, we find that the imaginary part of the amplitude for the production of real photons is larger than the imaginary part of the corresponding DIS amplitude by about a factor of 2, leading to the prediction of a significant counting rate for the current generation of experiments at HERA. We also find a large azimuthal angle asymmetry in $ep$ scattering for HERA kinematics which allows one to directly measure the real part of the DVCS amplitude and hence the nondiagonal parton distributions.

Diffractive exclusive photon production in DIS at DESY HERA

We demonstrate that perturbative QCD allows one to calculate the absolute cross section of diffractive exclusive production of photons at large $Q^2$ at HERA, while the aligned jet model allows one to estimate the cross section for intermediate $Q^2 \sim 2 GeV^2$. Furthermore, we find that the imaginary part of the amplitude for the production of real photons is larger than the imaginary part of the corresponding DIS amplitude by about a factor of 2, leading to the prediction of a significant counting rate for the current generation of experiments at HERA. We also find a large azimuthal angle asymmetry in $ep$ scattering for HERA kinematics which allows one to directly measure the real part of the DVCS amplitude and hence the nondiagonal parton distributions.

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 → γp′ in the limit of vanishing momentum transfer t = ( p′ − p) 2. The DVCS amplitude in this limit exhibits a scaling behavior described by two-argument distributions F( x, y) which specify the fractions of the initial momentum p and the momentum transfer r ≡ 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 flavor non-singlet part of the non-forward quark distribution.