2012/12/08 by Gernot Eichmann, Christian S. Fischer · 1 citation
Physics and Astronomy · #hep-ph #nucl-th
paper · pdf · doi:10.1103/physrevd.87.036006
36 pages, 10 figures, 5 tables
arxiv created 2012/12/08 · arxiv updated 2013/03/13
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.