Soft-photon spectra and the Low-Burnett-Kroll theorem

The study of next-to-leading-power (NLP) corrections in soft emissions continues to attract interest both in quantum chromodynamics (QCD) and in quantum electrodynamics (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 nonradiative 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 nonradiative 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msup><a:mrow><a:mi>e</a:mi></a:mrow><a:mrow><a:mo>+</a:mo></a:mrow></a:msup><a:msup><a:mrow><a:mi>e</a:mi></a:mrow><a:mrow><a:mo>−</a:mo></a:mrow></a:msup></a:mrow></a:math> annihilation and proton-proton collisions. Published by the American Physical Society 2024