Beam functions for N-jettiness at N3LO in perturbative QCD

Daniel Baranowski, Arnd Behring, Kirill Melnikov, Lorenzo Tancredi, Christopher Wever

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We present a calculation of all matching coefficients for N-jettiness beam functions at next-to-next-to-next-to-leading order (N3LO) in perturbative quantum chromodynamics (QCD). Our computation is performed starting from the respective collinear splitting kernels, which we integrate using the axial gauge. We use reverse unitarity to map the relevant phase-space integrals to loop integrals, which allows us to employ multi-loop techniques including integration-by-parts identities and differential equations. We find a canonical basis and use an algorithm to establish non-trivial partial fraction relations among the resulting master integrals, which allows us to reduce their number substantially. By use of regularity conditions, we express all necessary boundary constants in terms of an independent set, which we compute by direct integration of the corresponding integrals in the soft limit. In this way, we provide an entirely independent calculation of the matching coefficients which were previously computed in ref. [1].

Original languageEnglish
Article number73
JournalJournal of High Energy Physics
Issue number2
StatePublished - Feb 2023


  • Effective Field Theories of QCD
  • Factorization
  • Higher-Order Perturbative Calculations
  • Renormalization Group


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