Leading-Color Two-Loop Amplitudes for Four Partons and a W Boson in QCD

S. Abreu, F. Febres Cordero, H. Ita, M. Klinkert, B. Page, V. Sotnikov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present the leading-color two-loop QCD corrections for the scattering of four partons and a W boson, including its leptonic decay. The amplitudes are assembled from the planar two-loop helicity amplitudes for four partons and a vector boson decaying to a lepton pair, which are also used to determine the planar two-loop amplitudes for four partons and a Z/γ∗ boson with a leptonic decay. The analytic expressions are obtained by setting up a dedicated Ansatz and constraining the free parameters from numerical samples obtained within the framework of numerical unitarity. The large linear systems that must be solved to determine the analytic expressions are constructed to be in Vandermonde form. Such systems can be very efficiently solved, bypassing the bottleneck of Gaussian elimination. Our results are expressed in a basis of one-mass pentagon functions, which opens the possibility of their efficient numerical evaluation.
Original languageEnglish
Article number42
Pages (from-to)1-36
Number of pages36
JournalJournal of High Energy Physics
Issue number4
Publication statusPublished - 7 Apr 2022


  • hep-ph
  • Scattering Amplitudes
  • Electroweak Precision Physics
  • Higher-Order Perturbative Calculations


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