Soft-photon spectra and the LBK theorem

TL;DR

This paper examines the LBK theorem's consistency in soft-photon spectra, addressing ambiguities from momentum conservation and proposing a new formulation with numerical advantages, supported by results in muon pair production.

Contribution

It clarifies the ambiguity in the LBK theorem due to momentum conservation and introduces a modified formulation with shifted kinematics for easier numerical computation.

Findings

Different formulations of the LBK theorem are equivalent up to power-suppressed effects.

A new shifted kinematics approach simplifies numerical calculations.

Numerical results for soft-photon spectra in muon pair production are provided.

Abstract

The study of next-to-leading-power (NLP) corrections in soft emissions continues to attract interest both in QCD and in QED. Soft-photon spectra in particular provide a clean case-study for the experimental verification of the Low-Burnett-Kroll (LBK) theorem. In this paper we study the consistency of the LBK theorem in the context of an ambiguity arising from momentum-conservation constraints in the computation of non-radiative amplitudes. We clarify that this ambiguity leads to various possible formulations of the LBK theorem, which are all equivalent up to power-suppressed effects (i.e. beyond the formal accuracy of the LBK theorem). We also propose a new formulation of the LBK theorem with a modified shifted kinematics which facilitates the numerical computation of non-radiative amplitudes with publicly available tools. Furthermore, we present numerical results for soft-photon spectra in the associated production of a muon pair with a photon, both in $e^+e^-$ annihilation and proton-proton collisions.