Coherent enhancement of QED cross-sections in electromagnetic backgrounds

TL;DR

This paper introduces form factors to relate QED process amplitudes in vacuum to those in classical electromagnetic backgrounds, revealing coherent enhancements in cross sections that depend on background field properties and energy scaling.

Contribution

It presents a novel formalism using form factors to analyze QED processes in background fields, showing how cross sections are coherently enhanced and scale with energy.

Findings

Background fields cause coherent enhancement of QED cross sections.

Certain reaction channels show improved energy scaling in backgrounds.

Using x-ray free electron lasers can minimize kinematic suppression.

Abstract

We introduce form factors that relate the amplitude of a QED process in vacuum to its corresponding background-field process. The latter is characterised by a reduced S-matrix element where one or more photon field operators are replaced by classical background fields. In the associated Feynman diagram, external photon lines are supplanted with lines representing the c-number field. This modifies the cross section by factors proportional to powers of the Fourier amplitude of the classical field (and its complex conjugate). We demonstrate this explicitly by comparing different reaction channels of low-energy photon-photon scattering in a classical background. We find that background field cross sections typically undergo coherent enhancement and for some reaction channels display a more favourable scaling with centre-of-mass energy compared to the vacuum process. Similar coherent enhancement may be found for leading-order pair annihilation to one photon, but this competes with kinematic suppression. This suppression can be minimised by using an x-ray free electron laser as the classical background.