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arXiv · 2609.10069

On the universality of soft emission beyond the next-to-soft order

Martin Beneke·Maria Santana·Michel Stillger
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Abstract

The Low-Burnett-Kroll theorem (extended to non-abelian gauge theory) states that the tree-level emission amplitude of a soft gauge boson from an arbitrary hard process can be expressed in terms of the non-radiative amplitude including the next-to-soft term. Reformulating the soft theorem in the framework of an on-shell effective theory leads to a natural gauge-invariant split into an external and internal emission process to any order in the soft expansion. In this framework, we derive a compact expression for the all-order external emission amplitude expressed in terms of the non-radiative amplitude, and express the local emission amplitude through a single gauge-invariant operator at every order beyond the next-to-soft one. For scalar QCD, we compare the number of Lorentz- and $SU(3)$-invariant amplitudes for the radiative and non-radiative hard process with an arbitrary number of scalar quarks and antiquarks.

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Martin Beneke, Maria Santana, Michel Stillger. 2026-09-09. On the universality of soft emission beyond the next-to-soft order. https://arxiv.org/abs/2609.10069

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