HAL CCSD
Cuts from residues: the one-loop case
Abreu, Samuel
Britto, Ruth
Duhr, Claude
Gardi, Einan
Université de Fribourg = University of Fribourg (UNIFR)
Trinity College Dublin
Institut de Physique Théorique - UMR CNRS 3681 (IPHT) ; Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
Université Catholique de Louvain = Catholic University of Louvain (UCL)
CERN [Genève]
University of Edinburgh
cea-01468660
https://cea.hal.science/cea-01468660
https://cea.hal.science/cea-01468660/document
https://cea.hal.science/cea-01468660/file/1702.03163.pdf
https://cea.hal.science/cea-01468660
2017
ARXIV: 1702.03163
info:eu-repo/semantics/altIdentifier/arxiv/1702.03163
en
Feynman integrals
cut integrals
multivariate residues
homology theory
[PHYS]Physics [physics]
info:eu-repo/semantics/preprint
Preprints, Working Papers, ...
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.
2017-02-10
info:eu-repo/semantics/OpenAccess
European Project: 647356,H2020,ERC-2014-CoG,CutLoops(2015)
info:eu-repo/grantAgreement//647356/EU/Loop amplitudes in quantum field theory/CutLoops
European Project: 637019,H2020,ERC-2014-STG,MathAm(2015)
info:eu-repo/grantAgreement//637019/EU/Mathematical Structures in Scattering Amplitudes/MathAm