https://cea.hal.science/cea-01468660Abreu, SamuelSamuelAbreuUNIFR - Université de Fribourg = University of FribourgBritto, RuthRuthBrittoTrinity College DublinIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueDuhr, ClaudeClaudeDuhrUCL - Université Catholique de Louvain = Catholic University of LouvainCERN [Genève]Gardi, EinanEinanGardiUniversity of EdinburghCuts from residues: the one-loop caseHAL CCSD2017Feynman integralscut integralsmultivariate residueshomology theory[PHYS] Physics [physics]De Laborderie, EmmanuelleLoop amplitudes in quantum field theory - CutLoops - - H20202015-10-01 - 2020-10-01 - 647356 - VALID - Mathematical Structures in Scattering Amplitudes - MathAm - - H20202015-09-01 - 2020-08-31 - 637019 - VALID - 2017-02-15 16:25:032023-09-07 10:26:032017-02-16 14:25:35enPreprints, Working Papers, ...https://cea.hal.science/cea-01468660/documenttext/html; charset=utf-81Using 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.