3-point off-shell vertex in scalar QED in arbitrary gauge and dimension

TL;DR

This paper computes the full one-loop off-shell three-point scalar-photon vertex in scalar QED across arbitrary gauges and dimensions, providing explicit results and proposing non-perturbative forms consistent with perturbation theory.

Contribution

It offers the first complete calculation of the off-shell scalar-photon vertex in arbitrary gauge and dimension, including explicit results for 3D and 4D, and introduces non-perturbative proposals.

Findings

Explicit one-loop vertex expressions in 3D and 4D

Non-perturbative vertex forms matching perturbative results

Results applicable to both massive and massless scalars

Abstract

We calculate the complete one-loop off-shell three-point scalar-photon vertex in arbitrary gauge and dimension for Scalar Quantum Electrodynamics. Explicit results are presented for the particular cases of dimensions 3 and 4 both for massive and massless scalars. We then propose non-perturbative forms of this vertex that coincide with the perturbative answer to order $e^2$.