Cuts from residues: the one-loop case

Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi

Research output: Contribution to journalArticlepeer-review

Abstract

Using the multivariate residue calculus of Leray, we give a precise definition of the notion of a cut Feynman integral in dimensional regularization, as a residue evaluated on the variety where some of the propagators are put on shell. These are naturally associated to Landau singularities of the first type. Focusing on the one-loop case, we give an explicit parametrization to compute such cut integrals, with which we study some of their properties and list explicit results for maximal and next-to-maximal cuts. By analyzing homology groups, we show that cut integrals associated to Landau singularities of the second type are specific combinations of the usual cut integrals, and we obtain linear relations among different cuts of the same integral. We also show that all one-loop Feynman integrals and their cuts belong to the same class of functions, which can be written as parametric integrals.
Original languageEnglish
Article number114
Journal Journal of High Energy Physics
Volume1706
Issue number114
DOIs
Publication statusPublished - 21 Jun 2017

Keywords

  • hep-th
  • hep-ph

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