Rationalizing loop integration

Jacob L. Bourjaily, Andrew J. McLeod, Matt von Hippel, Matthias Wilhelm

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


We show that direct Feynman-parametric loop integration is possible for a large class of planar multi-loop integrals. Much of this follows from the existence of manifestly dual-conformal Feynman-parametric representations of planar loop integrals, and the fact that many of the algebraic roots associated with (e.g. Landau) leading singularities are automatically rationalized in momentum-twistor space — facilitating direct integration via partial fractioning. We describe how momentum twistors may be chosen non-redundantly to parameterize particular integrals, and how strategic choices of coordinates can be used to expose kinematic limits of interest. We illustrate the power of these ideas with many concrete cases studied through four loops and involving as many as eight particles. Detailed examples are included as supplementary material.

Original languageEnglish (US)
Article number184
JournalJournal of High Energy Physics
Issue number8
StatePublished - Aug 1 2018

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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