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

• DOI: 10.48550/arxiv.2405.07385
• Publication Date: 2024-09-20
• Authors: Patrick Copinger; James P. Edwards; Anton Ilderton; Karthik Rajeev
• Keywords: High Energy Physics - Theory; High Energy Physics - Phenomenology; High Energy Physics - Phenomenology (hep-ph); Nonperturbative Effects; High Energy Physics - Theory (hep-th); Nuclear and particle physics. Atomic energy. Radioactivity; FOS: Physical sciences; QC770-798; Scattering Amplitudes

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.