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Article
Report number	arXiv:1702.03163 ; CERN-TH-2017-033 ; CP3-17-05 ; Edinburgh-2017-05 ; FR-PHENO-2017-001
Title	Cuts from residues: the one-loop case
Related title	Cuts from residues: the one-loop case
Author(s)	Abreu, Samuel (Freiburg U.) ; Britto, Ruth (Trinity Coll., Dublin ; IPhT, Saclay) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys. ; Edinburgh U.)
Publication	2017-06-14
Imprint	2017-02-10
Number of pages	57
Note	v2: fixed minor typos in the normalisation of cut integrals
In:	JHEP 06 (2017) 114
DOI	10.1007/JHEP06(2017)114
Subject category	hep-ph ; Particle Physics - Phenomenology ; hep-th ; Particle Physics - Theory
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.
Copyright/License	arXiv nonexclusive-distrib. 1.0 Preprint: © 2017-2024 CERN (License: CC-BY-4.0)

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