Hadron Optics in Three-Dimensional Invariant Coordinate Space from Deeply Virtual Compton Scattering

TL;DR

This paper develops a covariant model of deeply virtual Compton scattering (DVCS) amplitudes to produce a three-dimensional, boost-invariant image of hadrons in light-front coordinate space, revealing diffraction patterns similar to optical scattering.

Contribution

It introduces a covariant model for DVCS amplitudes using QED one-loop fermion fluctuations and extends this to hadronic models via AdS/CFT, providing a novel 3D light-front imaging technique.

Findings

Fourier transforms of DVCS amplitudes show diffraction patterns.

The model produces a boost-invariant 3D image of hadrons in light-front space.

Diffractive features resemble optical wave scattering patterns.

Abstract

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.