Deeply Virtual Compton Scattering Amplitude Research Articles

Data-driven study of timelike Compton scattering

In the framework of collinear QCD factorization, the leading twist scattering amplitudes for deeply virtual Compton scattering (DVCS) and timelike Compton scattering (TCS) are intimately related thanks to analytic properties of leading and next-to-leading order amplitudes. We exploit this welcome feature to make data-driven predictions for TCS observables to be measured in near future experiments. Using a recent extraction of DVCS Compton form factors from most of the existing experimental data for that process, we derive TCS amplitudes and calculate TCS observables only assuming leading-twist dominance. Artificial neural network techniques are used for an essential reduction of model dependency, while a careful propagation of experimental uncertainties is achieved with replica methods. Our analysis allows for stringent tests of the leading twist dominance of DVCS and TCS amplitudes. Moreover, this study helps to understand quantitatively the complementarity of DVCS and TCS measurements to test the universality of generalized parton distributions, which is crucial e.g. to perform the nucleon tomography.

Twist-3 generalized parton distributions in deeply-virtual Compton scattering

The sub-leading power of the scattering amplitude for deeply-virtual Compton scattering (DVCS) off the nucleon contains leading-twist and twist-3 generalized parton distributions (GPDs). We point out that in DVCS, at twist-3 accuracy, one cannot address any individual twist-3 GPD. This complication appears on top of the deconvolution issues familiar from the twist-2 DVCS amplitude. Accessible are exclusively linear combinations involving both vector and axial-vector twist-3 GPDs. This implies, in particular, that the (kinetic) orbital angular momentum of quarks can hardly be constrained by twist-3 DVCS observables. Moreover, using the quark-target model, we find that twist-3 GPDs can be discontinuous. The discontinuities however cancel in the DVCS amplitude, which further supports the hypothesis of factorization at twist-3 accuracy.

A glimpse of gluons through deeply virtual compton scattering on the proton

The internal structure of nucleons (protons and neutrons) remains one of the greatest outstanding problems in modern nuclear physics. By scattering high-energy electrons off a proton we are able to resolve its fundamental constituents and probe their momenta and positions. Here we investigate the dynamics of quarks and gluons inside nucleons using deeply virtual Compton scattering (DVCS)—a highly virtual photon scatters off the proton, which subsequently radiates a photon. DVCS interferes with the Bethe-Heitler (BH) process, where the photon is emitted by the electron rather than the proton. We report herein the full determination of the BH-DVCS interference by exploiting the distinct energy dependences of the DVCS and BH amplitudes. In the regime where the scattering is expected to occur off a single quark, measurements show an intriguing sensitivity to gluons, the carriers of the strong interaction.

Skewness dependence of generalized parton distributions, conformal OPE, and the AdS/CFT correspondence

The traditional idea of the Pomeron/Reggeon description for hadron scattering is now being given theoretical foundation in gravity dual descriptions, where Pomeron corresponds to an exchange of spin-$j\ensuremath{\in}2\mathbb{Z}$ states in the graviton trajectory. Deeply virtual Compton scattering (DVCS) is essentially a two-to-two scattering process of a hadron and a photon, and hence one should be able to study nonperturbative aspects (the generalized parton distribution [GPD]) of this process by the Pomeron/Reggeon process in gravity dual. We find, however, that even one of the most developed formulations of gravity dual, Pomeron [Brower-Polchinski-Strassler-Tan (BPST), 2006], is not able to capture skewness dependence of GPD properly. Therefore, we compute Reggeon wave functions on ${\mathrm{AdS}}_{5}$ so that the formalism of BPST can be generalized. These wave functions are used to determine the DVCS amplitude, bring it to the form of conformal operator product expansion/collinear factorization, and extract a holographic model of GPD, which naturally fits into the framework known as ``dual parametrization,'' or the ``(conformal) collinear factorization approach.''

CONCEPTUAL ISSUES CONCERNING GENERALIZED PARTON DISTRIBUTIONS

We review the interface between the current theoretical framework based on generalized parton distributions (GPDs) and experimental measurements of deeply virtual Compton scattering (DVCS) observables. We find that the present theoretical framework needs to be extended to cover the current and future DVCS experiments. The current formulation is based on the quantum chromodynamics factorization of the handbag diagrams, relying on handbag dominance. Our examination reveals that the handbag diagrams by themselves do not satisfy electromagnetic gauge invariance. Our numerical estimates of the DVCS amplitudes in a solvable model indicate that the handbag contribution is not sufficient to saturate the exact result. Assuming the extraction of GPDs is made, we analyzed the crossover point in GPDs, important for the single spin asymmetry seen in DVCS experiments. We found that the inclusion of the higher Fock states is essential to explain the available data of single spin asymmetry.

From hard exclusive meson electroproduction to deeply virtual Compton scattering

We systematically evaluate observables for hard exclusive electroproduction of real photons and compare them to experiment using a set of Generalized Parton Distributions (GPDs) whose parameters are constrained by Deeply Virtual Meson Production data, nucleon form factors and parton distributions. The Deeply Virtual Compton Scattering amplitudes are calculated to leading-twist accuracy and leading order in QCD perturbation theory while the leptonic tensor is treated exactly, without any approximation. This study constitutes a check of the universality of the GPDs. We summarize all relevant details on the parametrizations of the GPDs and describe its use in the handbag approach of the aforementioned hard scattering processes. We observe a good agreement between predictions and measurements of deeply virtual Compton scattering on a wide kinematic range, including most data from H1, ZEUS, HERMES, Hall A and CLAS collaborations for unpolarized and polarized targets when available. We also give predictions relevant for future experiments at COMPASS and JLab after the 12 GeV upgrade.

On the mistake in the implementation of the minimal model of the dual parametrization and resulting inability to describe the high-energy deeply virtual Compton data

We correct the mistaken claim made by Guzey and Polyakov [Eur. Phys. J. C 46, 151 (2006) ] and Guzey and Teckentrup [Phys. Rev. D 74, 054027 (2006)] that the minimal model of the dual parametrization of nucleon generalized parton distributions gives a good, essentially model-independent description of high-energy data on deeply virtual Compton scattering (DVCS). In the implementation of the dual parametrization by Guzey-Polyakov and Guzey-Teckentrup (see above), the numerical prefactor of two in front of the DVCS amplitude was missing. We show that the corrected minimal model of the dual parametrization significantly overestimates the Hadron Electron Ring Accelerator data (H1 and ZEUS experiments) on the DVCS cross section.

Deeply Virtual Compton Scattering on nucleons and nuclei in the Generalized Vector Meson Dominance model

We consider Deeply Virtual Compton Scattering (DVCS) on nucleons and nuclei in the framework of the Generalized Vector Meson Dominance (GVMD) model. We demonstrate that the GVMD model provides a good description of the HERA data on the dependence of the proton DVCS cross-section on Q2, W (at Q 2 = 4 GeV^2) and t . At Q 2 = 8 GeV^2, the soft W -behavior of the GVMD model somewhat underestimates the W -dependence of the DVCS cross-section due to the hard contribution not present in the GVMD model. We estimate 1/Q 2 power-suppressed corrections to the DVCS amplitude and the DVCS cross-section and find them large. We also make predictions for the nuclear DVCS amplitude and cross-section in the kinematics of the future Electron-Ion Collider. We predict significant nuclear shadowing, which matches well predictions of the leading-twist nuclear shadowing in DIS on nuclei.

Deeply Virtual Compton Scattering off the Neutron

The present experiment exploits the interference between the deeply virtual Compton scattering (DVCS) and the Bethe-Heitler processes to extract the imaginary part of DVCS amplitudes on the neutron and on the deuteron from the helicity-dependent D(e,e'gamma)X cross section measured at Q2=1.9 GeV2 and xB=0.36. We extract a linear combination of generalized parton distributions (GPDs) particularly sensitive to E_{q}, the least constrained GPD. A model dependent constraint on the contribution of the up and down quarks to the nucleon spin is deduced.

Beam-charge azimuthal asymmetry and deeply virtual Compton scattering

The first observation of an azimuthal cross--section asymmetry with respect to the charge of the incoming lepton beam is reported from a study of hard exclusive electroproduction of real photons. The data have been accumulated by the HERMES experiment at DESY, in which the HERA 27.6 GeV electron or positron beam scattered off an unpolarized hydrogen gas target. The observed asymmetry is attributed to the interference between the Bethe--Heitler process and the Deeply Virtual Compton Scattering (DVCS) process. The interference term is sensitive to DVCS amplitudes, which provide the most direct access to Generalized Parton Distributions.

Hadron optics: Diffraction patterns in deeply virtual Compton scattering

We show that the Fourier transform of the Deeply Virtual Compton Scattering (DVCS) amplitude with respect to the skewness variable {zeta} provides a unique way to visualize the light-front wavefunctions (LFWFs) of the target state in the boost-invariant longitudinal coordinate space variable ({sigma} = P{sup +}y{sup -}/2). The results are analogous to the diffractive scattering of a wave in optics in which the dependence of the amplitude on {sigma} measures the physical size of the scattering center of a one-dimensional system. If one combines this longitudinal transform with the Fourier transform of the DVCS amplitude with respect to the transverse momentum transfer {Delta}{sup {perpendicular}}, one can obtain a complete three-dimensional description of hadron optics at fixed light-front time {tau} = t + z/c. As a specific example, we utilize the quantum fluctuations of a fermion state at one loop in QED to obtain the behavior of the DVCS amplitude for electron-photon scattering. We then simulate the wavefunctions for a hadron by differentiating the above LFWFs with respect to M{sup 2} and study the corresponding DVCS amplitudes in {sigma} space.

On the A-dependence of nuclear generalized parton distributions

We perform a microscopic evaluation of nuclear generalized parton distributions (GPDs) for spin-0 nuclei in the framework of the Walecka model. We demonstrate that the meson (non-nucleon) degrees of freedom dramatically influence nuclear GPDs, which is revealed in the non-trivial and unexpected A-dependence of deeply virtual Compton scattering (DVCS) observables. In particular, we find that the first moment of the nuclear D-term dA(0) ∝ A2.26, which confirms the earlier prediction of Polyakov. We find that in the HERMES kinematics, contrary to the free proton case, the nuclear meson degrees of freedom in large nuclei enhance the nuclear DVCS amplitude which becomes comparable to the Bethe–Heitler amplitude and, thus, give the non-trivial A-dependence to the DVCS asymmetries: as a function of the atomic number, the beam–charge asymmetry increases whereas the beam–spin asymmetry decreases slowly.

Current status and future measurements of DVCS at HERMES

Sizable beam-spin, target-spin and beam-charge azimuthal asymmetries in hard electroproduction of photons have been measured at the HERMES experiment using the 27.6 GeV HERA electron beam. The observed asymmetries are attributed to the interference of the Bethe-Heitler and Deeply Virtual Compton Scattering (DVCS) processes. Polarized hydrogen and deuterium targets are used to access the DVCS amplitudes of protons and neutrons. In addition, HERMES observed for the first time DVCS amplitudes which appear in the coherent scattering off nuclei. In 2005, the HERMES spectrometer will be upgraded by a recoil detector to measure the recoiling proton and thus identify the complete final state of the DVCS process. With improved kinematic resolution and background suppression HERMES aims to access the Generalized Parton Distributions (GPDs) of protons and neutrons and possibly those of nuclear states.

Generalized Parton Distributions, Analyticity and Crossing

A simple procedure for the derivation of Generalized Parton Distributions (GPDs) is suggested. Factorization of the perturbative and non-perturbative parts of the scattering amplitude is not assumed. Instead, GPDs are related, in the first approximation, to the deeply virtual Compton scattering (DVCS) amplitude, the emphasis being on the construction of DVCS or meson production amplitudes with correct analytical properties in a wide range of the kinematical variables.

Detailed QCD analysis of twist-3 effects in deeply virtual Compton scattering observables

In this paper I present a detailed QCD analysis of twist-3 effects in the Wandzura-Wilczek (WW) approximation in deeply virtual Compton scattering (DVCS) observables for various kinematical settings, representing the DESY HERA, HERMES, CLAS and the planned EIC (electron-ion-collider) experiments. I find that the twist-3 effects in the WW approximation are almost always negligible at collider energies but can be large for low ${Q}^{2}$ and smaller ${x}_{\mathrm{bj}}$ in observables for the lower energy, fixed target experiments directly sensitive to the real part of DVCS amplitudes like the charge asymmetry. Conclusions are then drawn about the reliability of extracting twist-2 generalized parton distributions (GPDs) from experimental data and a first, phenomenological, parametrization of the LO and NLO twist-2 GPD H, describing all the currently available DVCS data within the experimental errors is given.

Deeply virtual Compton scattering and saturation approach

We investigate the deeply virtual Compton scattering (DVCS) in the color dipole approach, implementing the dipole cross section through the saturation model, which interpolates successfully between soft and hard regimes. The imaginary and real part of the DVCS amplitude are obtained and the results are compared to the available data.

Continuity of generalized parton distributions for the pion virtual Compton scattering

We discuss a consistent treatment of the light-front gauge-boson and meson wave functions in the analyses of the generalized parton distributions(GPDs) and the scattering amplitudes in deeply virtual Compton scattering(DVCS) for the pion. The continuity of the GPDs at the crossover, where the longitudinal momentum fraction of the probed quark is same with the skewedness parameter, and the finiteness of the DVCS amplitude are ensured if the same light-front radial wave function as that of the meson bound state wave function is used for the gauge boson bound state arising from the pair-creation(or nonvalence) diagram. The frame-independence of our model calculation is also guaranteed by the constraint from the sum rule between the GPDs and the form factors.

Next-to-leading order QCD analysis of deeply virtual Compton scattering amplitudes

We present a next-to-leading order (NLO) QCD analysis of unpolarized and polarized deeply virtual Compton scattering (DVCS) amplitudes, for two different input scenarios, in the $\bar{MS}$ scheme. We illustrate and discuss the size of the NLO effects and the behavior of the amplitudes in skewedness, $\zeta$, and photon virtuality, $Q^2$. In the unpolarized case, at fixed $Q^2$, we find a remarkable effective power-law behaviour in $\zeta$, akin to Regge factorization, over several orders of magnitude in $\zeta$. We also quantify the ratio of real to imaginary parts of the DVCS amplitudes and their sensitivity to changes of the factorization scale.

Factorization in deeply virtual Compton scattering: local OPE formalism and structure functions

We give a complete treatment of factorization of deeply virtual Compton scattering (DVCS) in the generalized Bjorken limit, using the local operator product expansion. The method allows a straightforward proof that, at leading twist, the DVCS amplitude factorizes into an integral over coefficient functions and skewed parton distribution functions. The integral is well defined for on-shell final state photons if the Wilson coefficients satisfy a certain factorization condition, which we derive. We also show that it enables a simple proof that soft singularities either cancel out or, in the case where the final state photon is on shell, are integrable. This confirms the argument of Collins and Freund. Further, we repeat the tree-level calculation of twist-three contributions to DVCS off a scalar target, where factorization was found to be violated. We propose a new definition of the structure functions and calculate the coefficient functions, which are such that factorization works.

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, for the tensor amplitude T μν , this approximation gives a finite result for the longitudinal polarization of the virtual photon and a divergent result in case of transverse polarization. However, the divergent part has zero projection onto the polarization vector of the final real photon.