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{sup 2}/2p {center_dot} 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 {rvec b}{sub {perpendicular}}, thus providing a light-front ''photograph'' of the target hadron in a frame-independent three-dimensional light-front 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.