All-multiplicity amplitudes in impulsive PP-waves from the worldline formalism

TL;DR

This paper derives new master formulae for tree-level scattering amplitudes involving multiple photons in impulsive PP-waves using the worldline formalism, revealing novel factorization structures and averaging properties.

Contribution

It introduces Bern-Kosower type master formulae for multi-photon scattering in impulsive PP-waves, extending single-photon results to arbitrary multiplicity with non-perturbative coupling treatment.

Findings

Amplitudes can be expressed as vacuum currents with an averaged single photon.

Currents and amplitudes are averages over impulsive plane wave backgrounds.

New factorization structures simplify the all-orders interaction analysis.

Abstract

We use the worldline formalism to derive Bern-Kosower type Master Formulae for the tree-level scattering of a charged particle and an arbitrary number of photons on impulsive PP-waves, where the coupling of the PP-wave to matter is treated fully non-perturbatively. We show that, in a certain kinematic regime characterised by a semi-classical positive energy condition, both off-shell currents and scattering amplitudes exhibit two novel factorisation structures. First, they may be written as currents in vacuum but with a single additional photon, averaged over the momentum of that photon. This converts the all-orders interaction with the PP-wave into a single effective interaction. Second, the currents and amplitudes may be written as a weighted average of the corresponding quantities in an impulsive plane wave background, with the average taken over all possible field strengths of the plane wave. This generalises a known single-photon result to arbitrary multiplicity.