Cuts from residues: the one-loop case

  • Samuel AbreuEmail author
  • Ruth Britto
  • Claude Duhr
  • Einan Gardi
Open Access
Regular Article - Theoretical Physics


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.


Scattering Amplitudes Perturbative QCD 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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© The Author(s) 2017

Authors and Affiliations

  1. 1.Physikalisches InstitutAlbert-Ludwigs-Universität FreiburgFreiburgGermany
  2. 2.School of MathematicsTrinity CollegeDublin 2Ireland
  3. 3.Hamilton Mathematics InstituteTrinity CollegeDublin 2Ireland
  4. 4.Institut de Physique Théorique, Université Paris Saclay, CEA, CNRSGif-sur-YvetteFrance
  5. 5.Theoretical Physics DepartmentCERNGenevaSwitzerland
  6. 6.Center for Cosmology, Particle Physics and Phenomenology (CP3)Université Catholique de LouvainLouvain-La-NeuveBelgium
  7. 7.Higgs Centre for Theoretical Physics, School of Physics and AstronomyUniversity of EdinburghEdinburghU.K.

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