One-loop multicollinear limits from 2-point amplitudes on self-dual backgrounds

TL;DR

This paper explores the multicollinear limits of one-loop vacuum amplitudes in self-dual backgrounds, revealing helicity restrictions and confirming the absence of vacuum birefringence in supersymmetric gauge theories.

Contribution

It introduces a method to derive multicollinear limits of one-loop amplitudes in self-dual backgrounds, highlighting helicity restrictions and extending known birefringence results.

Findings

Only the all-plus helicity amplitude survives in multicollinear limits.

No helicity flip occurs in supersymmetric gauge theories on plane wave backgrounds.

Results are consistent with known vacuum amplitudes.

Abstract

For scattering amplitudes in strong background fields, it is -- at least in principle -- possible to perturbatively expand the background to obtain higher-point vacuum amplitudes. In the case of self-dual plane wave backgrounds we consider this expansion for two-point, one-loop amplitudes in pure Yang-Mills, QED and QCD. This enables us to obtain multicollinear limits of 1-loop vacuum amplitudes; the resulting helicity configurations are surprisingly restricted, with only the all-plus helicity amplitude surviving. These results are shown to be consistent with well-known vacuum amplitudes. We also show that for both abelian and non-abelian supersymmetric gauge theories, there is no helicity flip (and hence no vacuum birefringence) on any plane wave background, generalising a result previously known in the Euler-Heisenberg limit of super-QED.