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PreprintCC BY 4.0arXiv

All three-loop four-point massless integrals with one off-shell leg

  • Thomas Gehrmann
  • Petr Jakubčík
  • Jungwon Lim
  • Andreas von Manteuffel
  • Cesare Carlo Mella
  • Lorenzo Tancredi
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Abstract

We present the complete set of massless three-loop four-point master integrals with one off-shell external leg. These are essential building blocks for the three-loop virtual corrections to Higgs-boson or vector-boson production in association with a jet at the Large Hadron Collider, required for next-to-next-to-next-to-leading-order QCD predictions. We construct a complete basis of canonical integrals by identifying integrands with simple poles and unit leading singularities, solely by integrand analysis. This includes an integral family with 371 master integrals and a 19-dimensional top sector. The solutions for all relevant integrals are provided as a map to a minimal set of iterated integrals graded according to their analytic properties, together with high-precision series expansions.

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Cite

BibTeXRIS
BibTeX
@misc{gehrmann2026threeloop,
  title = {{All three-loop four-point massless integrals with one off-shell leg}},
  author = {Thomas Gehrmann and Petr Jakubčík and Jungwon Lim and Andreas von Manteuffel and Cesare Carlo Mella and Lorenzo Tancredi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20820},
  eprint = {2610.20820},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20820},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - All three-loop four-point massless integrals with one off-shell leg
AU  - Thomas Gehrmann
AU  - Petr Jakubčík
AU  - Jungwon Lim
AU  - Andreas von Manteuffel
AU  - Cesare Carlo Mella
AU  - Lorenzo Tancredi
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20820
UR  - https://arxiv.org/abs/2610.20820
AB  - We present the complete set of massless three-loop four-point master integrals with one off-shell external leg. These are essential building blocks for the three-loop virtual corrections to Higgs-boson or vector-boson production in association with a jet at the Large Hadron Collider, required for next-to-next-to-next-to-leading-order QCD predictions. We construct a complete basis of canonical integrals by identifying integrands with simple poles and unit leading singularities, solely by integrand analysis. This includes an integral family with 371 master integrals and a 19-dimensional top sector. The solutions for all relevant integrals are provided as a map to a minimal set of iterated integrals graded according to their analytic properties, together with high-precision series expansions.
ER  -