On the Compton scattering vertex for massive scalar QED

TL;DR

This paper constructs a non-perturbative form of the Compton scattering vertex in massive scalar QED, ensuring consistency with fundamental identities and calculating complex integrals for general kinematics.

Contribution

It provides a non-perturbative construction of the Compton scattering vertex in scalar QED, including detailed evaluation of the transverse part at one-loop order for general kinematics.

Findings

Derived the non-perturbative vertex consistent with WFGTI.

Calculated complex 4-point integrals with three massive propagators.

Discussed potential applications of the vertex in quantum field theory.

Abstract

We investigate the Compton scattering vertex of charged scalars and photons in scalar quantum electrodynamics (SQED). We carry out its non perturbative construction consistent with Ward-Fradkin-Green-Takahashi identity (WFGTI) which relates 3-point vertices to the 4-point ones. There is an undetermined part which is transverse to one or both the external photons, and needs to be evaluated through perturbation theory. We present in detail how the transverse part at the 1-loop order can be evaluated for completely general kinematics of momenta involved in covariant gauges and dimensions. This involves the calculation of genuine 4-point functions with three massive propagators, the most non-trivial integrals reported in this paper. We also discuss possible applications of our results.