Cutting rules in strong field QED with application to trident pair production

TL;DR

This paper develops a general cutting equation for QED in strong fields, connecting radiative corrections to pair production rates, and provides a detailed analytical expression for the trident process.

Contribution

It introduces a universal cutting rule framework for strong field QED, applicable at any loop order and potentially extendable to nonperturbative regimes.

Findings

Established that total rates can be derived from higher-loop corrections using cutting rules.

Provided a complete analytical expression for the trident process rate, including spin effects.

Highlighted the need for careful reconstruction of differential rates from higher-loop data.

Abstract

Following Veltman's approach, we formulate and discuss a general cutting equation for QED in a plane-wave background. We apply the corresponding cutting rules to justify the connection between the two-loop radiative corrections to elastic electron scattering and the rate of the trident process in a constant crossed field. As a byproduct, we compare the previously published results for the trident process in a constant crossed field and present a complete analytical expression for direct and exchange contributions to its rate, which is resolved in the spin of the initial electron. Our findings establish that although total rates can be reliably extracted from higher-loop by applying the cutting rules, reconstruction of differential rates requires additional care. The cutting rules apply to any loop order and may be extended to nonperturbative regimes.