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
arxiv:1702.03163
[CEA] CEA - Commissariat à l'énergie atomique
[CNRS] CNRS - Centre national de la recherche scientifique
[OPENAIRE] OpenAIRE
[DSM-IPHT] IPHT
[CEA-UPSAY] CEA - Université Paris-Saclay
[UNIV-PARIS-SACLAY] Université Paris-Saclay
[CEA-UPSAY-SACLAY] CEA-UPSAY-SACLAY
[CEA-DRF] Direction de Recherche Fondamentale
[TEST-HALCNRS] Collection test HAL CNRS
[GS-MATHEMATIQUES] Graduate School Mathématiques
[GS-PHYSIQUE] Graduate School Physique
Cuts from residues: the one-loop case
Abreu, Samuel
Britto, Ruth
Duhr, Claude
Gardi, Einan
[PHYS] Physics [physics]
UNDEFINED
Feynman integrals
cut integrals
multivariate residues
homology theory
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
2017-02-15
en