Diffraction Patterns in Deeply Virtual Compton Scattering

We report on a calculation to show that the Fourier transform of the Deeply Virtual Compton Scattering (DVCS) amplitude with respect to the skewness variable \zeta at fixed invariant momentum transfer squared t gives results that are analogous to the diffractive scattering of a wave in optics. 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^2 and study the corresponding DVCS amplitudes in light-front longitudinal space.Comment: Presented at the 17 th International Spin Physics Symposium, Kyoto, Japan, October 2-7, 200

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 $\zeta$ at fixed invariant momentum transfer squared $t$ provides a unique way to visualize the structure of the target hadron in the boost-invariant longitudinal coordinate space. The results are analogous to the diffractive scattering of a wave in optics. 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 $M^2$ and study the corresponding DVCS amplitudes in light-front longitudinal space. In both cases we observe that the diffractive patterns in the longitudinal variable conjugate to $\zeta$ sharpen and the positions of the first minima move in with increasing momentum transfer. For fixed $t$, higher minima appear at positions which are integral multiples of the lowest minimum. Both these observations strongly support the analogy with diffraction in optics.Comment: Some plots modified, clarifications and references adde

Sum rules and dualities for generalized parton distributions: is there a holographic principle?

To leading order approximation, the physical content of generalized parton distributions (GPDs) that is accessible in deep virtual electroproduction of photons or mesons is contained in their value on the cross-over trajectory. This trajectory separates the t-channel and s-channel dominated GPD regions. The underlying Lorentz covariance implies correspondence between these two regions through their relation to GPDs on the cross-over trajectory. This point of view leads to a family of GPD sum rules which are a quark analogue of finite energy sum rules and it guides us to a new phenomenological GPD concept. As an example, we discuss the constraints from the JLab/Hall A data on the dominant u-quark GPD H. The question arises whether GPDs are governed by some kind of holographic principle.Comment: 45 pages, 4 figures, Sect. 2 reorganized for clarity. Typos in Eq. (20) corrected. 4 new refs. Matches published versio

Generalized Parton Distributions from Hadronic Observables: Non-Zero Skewness

We propose a physically motivated parametrization for the unpolarized generalized parton distributions, H and E, valid at both zero and non-zero values of the skewness variable, \zeta. Our approach follows a previous detailed study of the \zeta=0 case where H and E were determined using constraints from simultaneous fits of the experimental data on both the nucleon elastic form factors and the deep inelastic structure functions in the non singlet sector. Additional constraints at \zeta \neq 0 are provided by lattice calculations of the higher moments of generalized parton distributions. We illustrate a method for extracting generalized parton distributions from lattice moments based on a reconstruction using sets of orthogonal polynomials. The inclusion in our fit of data on Deeply Virtual Compton Scattering is also discussed. Our method provides a step towards a model independent extraction of generalized distributions from the data. It also provides an alternative to double distributions based phenomenological models in that we are able to satisfy the polynomiality condition by construction, using a combination of experimental data and lattice, without resorting to any specific mathematical construct.Comment: 29 pages, 8 figures; added references, changed text in several place

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 \zeta= Q^2/ 2 p.q can be used to provide an image of the target hadron in the boost-invariant variable \sigma, the coordinate conjugate to light-front time \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 wavefunctions of a lepton in \sigma space. A consistent model for hadronic amplitudes can then be obtained by differentiating the light-front wavefunctions with respect to the bound-state mass. The resulting DVCS helicity amplitudes are evaluated as a function of \sigma and the impact parameter \vec b_\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 \sigma measures the physical size of the scattering center in a one-dimensional system.Comment: minor modification to text, preprint number update

The longitudinal cross section of vector meson electroproduction

We analyze electroproduction of light vector mesons (V=rho, phi and omega) at small Bjorken-x in the handbag approach in which the process factorizes into general parton distributions and partonic subprocesses. The latter are calculated in the modified perturbative approach where the transverse momenta of the quark and antiquark forming the vector meson are retained and Sudakov suppressions are taken into account. Modeling the generalized parton distributions through double distributions and using simple Gaussian wavefunctions for the vector mesons, we compute the longitudinal cross sections at large photon virtualities. The results are in fair agreement with the findings of recent experiments performed at HERA and HERMES.Comment: 27 pages, 20 figures, using LATEX with graphic