Femto-Photography of Protons to Nuclei with Deeply Virtual Compton Scattering

Developments in deeply virtual Compton scattering allow the direct measurements of scattering amplitudes for exchange of a highly virtual photon with fine spatial resolution. Real-space images of the target can be obtained from this information. Spatial resolution is determined by the momentum transfer rather than the wavelength of the detected photon. Quantum photographs of the proton, nuclei, and other elementary particles with resolution on the scale of a fraction of a femtometer is feasible with existing experimental technology. More than 40 years ago, elastic scattering of relativistic electrons from protons by Hofstadter[1] et al probed the dimensions of protons and nuclei. On general principles the scattering is governed by “form factors”, which parameterize the difference between point-like scattering and the observations. In static non-relativistic approximations of the era, the form factors were interpreted as “. . . determining the distribution of charge and magnetic moment in the nuclei of atoms and of the nucleons themselves”[2], with the experiments receiving the Nobel Prize in 1961. The charge radius was found to be about 0.7 femtometer. The neutron’s form factor was later interpreted in terms of a positively charged core surrounded by a negatively charged outer shell. In retrospect, these classic interpretations are open to doubt. Neither the impulse approximation nor the interpretation as charge density applies so simply to hadronic physics in the regime of the experiments. Point-like structure now attributed to quarks has been deduced indirectly, in conjunction with the development of Quantum Chromodynamics and deeply inelastic scattering experiments (DIS). The structure of hadrons as complex aggregates of quarks remains rather mysterious. Deeply virtual Compton scattering (DVCS)[3] combines features of the inelastic processes with those of an elastic process. A relativistic charged lepton (electron, positron, or possibly a muon) is scattered from a target nucleon or nucleus. A real photon of 4-momentum q μ = (q ′ 0, ~q ) is also observed in the final state. With e(k), e(k) denoting the initial and final electrons of momenta k, k respectively, and P, P ′ denoting the momentum of the target, the process is e(k) + P → e(k) + P ′ + γ(q).