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  • Letter
  • Open Access

Canonical differential equations for the elliptic two-loop five-point integral family relevant to tt¯+jet production at leading color

Matteo Becchetti1, Christoph Dlapa2, and Simone Zoia3

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Phys. Rev. D 112, L031501 – Published 21 August, 2025

DOI: https://doi.org/10.1103/zt4w-c1jk

Abstract

We complete the construction of canonical differential equations (DEs) for all families of Feynman integrals appearing in the two-loop leading-color QCD amplitude for top-pair production in association with a jet at hadron colliders. This allows us to obtain analytic results for all required Feynman integrals in terms of iterated integrals with closed-form kernels. To achieve this, we study the two-loop five-point integral family for which canonical DEs were previously unavailable due to the appearance of elliptic functions and nested square roots. In addition to marking a significant step toward next-to-next-to-leading-order QCD predictions for a high-priority LHC process, this is the first time that canonical DEs are obtained for Feynman integrals where elliptic functions appear in conjunction with the high algebraic complexity of a process with more than four particles. Our results also reveal a number of new interesting analytic features, such as a “duplet” structure that generalizes the even/odd parity of square roots to nested square roots.

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Phys. Rev. D 112, L031501– Published 21 August, 2025
  • Received 13 March 2025
  • Accepted 31 July 2025
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