Dispersion representations for hard exclusive processes

TL;DR

This paper investigates the dispersion relations in hard exclusive scattering processes, analyzing their consistency at all perturbative orders and exploring how they can be used to extract information about generalized parton distributions.

Contribution

It provides a detailed analysis of dispersion relations for amplitudes and kernels, offering insights into GPD extraction and model consistency checks.

Findings

Dispersion relations hold at all orders in perturbation theory.

Real and imaginary parts of amplitudes reveal GPD information.

Model consistency can be tested via dispersion relation analysis.

Abstract

Several hard exclusive scattering processes admit a description in terms of generalized parton distributions and perturbative hard-scattering kernels. Both the physical amplitude and the hard-scattering kernels fulfill dispersion relations. We give a detailed investigation of their consistency at all orders in perturbation theory. The results shed light on the information about generalized parton distributions that can be extracted from the real and imaginary parts of exclusive amplitudes. They also provide a practical consistency check for models of these distributions in which Lorentz invariance is not exactly satisfied.