Multiple soft-photon emission at next-to-leading power to all orders

TL;DR

This paper develops an all-orders next-to-leading power soft theorem for multi-photon emission in QED, simplifying complex multi-emission amplitudes and validating the theorem through explicit calculations in muon-electron scattering.

Contribution

It generalizes the soft photon theorem to NLP for multiple emissions to all orders, extending previous leading-power results and providing a new framework for precise QED calculations.

Findings

Derived the NLP soft theorem for multi-photon emission to all orders.

Proved that double-emission contributions are tree-level exact.

Calculated electron-line corrections in muon-electron scattering at NLP.

Abstract

This paper derives a next-to-leading power (NLP) soft theorem for multi-photon emission to all orders in the electromagnetic coupling constant, generalising the leading-power theorem of Yennie, Frautschi, and Suura. Working in the QED version of heavy-quark effective theory, multi-emission amplitudes are shown to reduce to single- and double-radiation contributions only. Single soft-photon emission, in turn, is described by the recent all-order extension of the Low-Burnett-Kroll theorem, where the tree-level formula is supplemented with a one-loop exact soft function. The same approach is used in this article to prove that the genuine double-emission contribution is tree-level exact. As a validation and a first non-trivial application of the multi-photon theorem, the real-real-virtual electron-line corrections to muon-electron scattering are calculated at NLP in the soft limit.