Nucleon Compton scattering in the Dyson-Schwinger approach

TL;DR

This paper investigates nucleon Compton scattering using the Dyson-Schwinger/Faddeev framework, deriving a consistent fermion two-photon vertex and calculating the scattering amplitude including key nonperturbative effects.

Contribution

It introduces a detailed analysis of the quark Compton vertex, ensuring Ward-Takahashi identity compliance, and implements it in the nucleon scattering amplitude within a nonperturbative approach.

Findings

Reproduces pion-photon transition form factor near the pion pole.

Derives a kinematically regular fermion two-photon vertex.

Provides a consistent nonperturbative calculation of nucleon Compton scattering.

Abstract

We analyze the nucleon's Compton scattering amplitude in the Dyson-Schwinger/Faddeev approach. We calculate a subset of diagrams that implements the nonperturbative handbag contribution as well as all t-channel resonances. At the quark level, these ingredients are represented by the quark Compton vertex whose analytic properties we study in detail. We derive a general form for a fermion two-photon vertex that is consistent with its Ward-Takahashi identities and free of kinematic singularities, and we relate its transverse part to the onshell nucleon Compton amplitude. We solve an inhomogeneous Bethe-Salpeter equation for the quark Compton vertex in rainbow-ladder truncation and implement it in the nucleon Compton scattering amplitude. The remaining ingredients are the dressed quark propagator and the nucleon's bound-state amplitude which are consistently solved from Dyson-Schwinger and covariant Faddeev equations. We verify numerically that the resulting quark Compton vertex and nucleon Compton amplitude both reproduce the pion-photon transition form factor when the pion pole in the t-channel is approached.