Universal structure of radiative QED amplitudes at one loop

TL;DR

This paper extends the Low-Burnett-Kroll theorem to one-loop QED amplitudes and derives a one-loop collinear splitting function, improving the understanding and numerical stability of radiative corrections in soft and collinear regimes.

Contribution

It provides the first explicit one-loop relation between radiative and non-radiative amplitudes in the soft limit and introduces a one-loop collinear splitting function for QED.

Findings

Extended Low-Burnett-Kroll theorem to one-loop level

Derived one-loop collinear splitting function in QED

Enhanced numerical stability in soft and collinear phase-space regions

Abstract

We present two novel results about the universal structure of radiative QED amplitudes in the soft and in the collinear limit. On the one hand, we extend the well-known Low-Burnett-Kroll theorem to the one-loop level and give the explicit relation between the radiative and non-radiative amplitude at subleading power in the soft limit. On the other hand, we consider a factorisation formula at leading power in the limit where the emitted photon becomes collinear to a light fermion and provide the corresponding one-loop splitting function. In addition to being interesting in their own right these findings are particularly relevant in the context of fully-differential higher-order QED calculations. One of the main challenges in this regard is the numerical stability of radiative contributions in the soft and collinear regions. The results presented here allow for a stabilisation of real-virtual amplitudes in these delicate phase-space regions by switching to the corresponding approximation without the need of explicit computations.