Nucleon Compton scattering from the Dyson-Schwinger perspective

TL;DR

This paper presents a nonperturbative Dyson-Schwinger approach to nucleon Compton scattering, introducing a covariant tensor basis and calculating the amplitude including meson resonances, with applications to form factors.

Contribution

It introduces a kinematic-singularity-free tensor basis and computes the nonperturbative Compton amplitude at the quark-gluon level using Dyson-Schwinger equations.

Findings

Reproduces the pi-gamma-gamma transition form factor.

Includes all t-channel meson resonances.

Validates the approach with known form factor results.

Abstract

We summarize results from our recent paper* on nucleon Compton scattering in the Dyson-Schwinger approach. We study the Compton scattering phase space and its various kinematic limits, and we introduce a covariant, transverse tensor basis for the scattering amplitude that is free of kinematic singularities. We illustrate the decomposition of the Compton amplitude at the quark-gluon level and calculate its nonperturbative handbag part, which also includes all t-channel meson resonances. The calculation requires numerical solutions for the dressed quark propagator, the nucleon's Faddeev amplitude and the quark Compton vertex as its input; they are consistently obtained from Dyson-Schwinger, Bethe-Salpeter and Faddeev equations. As a first application, we verify that the result for the Compton scattering amplitude reproduces the pi-gamma-gamma transition form factor when the pion pole in the t channel is approached. *G. Eichmann and C. S. Fischer, arXiv:1212.1761 [hep-ph].