The LBK theorem to all orders

TL;DR

This paper extends the Low-Burnett-Kroll theorem to all orders in perturbation theory within heavy-quark effective theory, showing that soft photon emissions at next-to-leading power are determined by non-radiative amplitudes, simplifying calculations.

Contribution

It generalizes the LBK theorem to all orders in perturbation theory for unpolarised scattering, providing a method to compute radiative corrections using the non-radiative amplitude.

Findings

Soft theorem at NLP determined by non-radiative amplitude

Virtual corrections vanish beyond one loop in the effective theory

Explicit calculation of electron-line corrections in muon-electron scattering

Abstract

We study the soft limit of one-photon radiation at next-to-leading power (NLP) in the framework of heavy-quark effective theory (HQET) to all orders in perturbation theory. We establish the soft theorem that for unpolarised scattering the radiative contribution up to NLP is entirely determined by the non-radiative amplitude. This generalises the Low-Burnett-Kroll (LBK) theorem for QED to all orders. All hard matching corrections can be calculated by applying the LBK differential operator to the non-radiative amplitude. The virtual corrections in the effective theory vanish beyond one loop, resulting in a one-loop exact soft function. As a first, non-trivial application we calculate the real-virtual-virtual electron-line corrections to muon-electron scattering at NLP in the soft limit.