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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{beneke2026universality,
  title = {{On the universality of soft emission beyond the next-to-soft order}},
  author = {Martin Beneke and Maria Santana and Michel Stillger},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10069},
  eprint = {2609.10069},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10069},
}
RIS
TY  - UNPB
TI  - On the universality of soft emission beyond the next-to-soft order
AU  - Martin Beneke
AU  - Maria Santana
AU  - Michel Stillger
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10069
UR  - https://arxiv.org/abs/2609.10069
AB  - 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.
ER  -