Cuts from residues: the one-loop case
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Publication:683231
DOI10.1007/JHEP06(2017)114zbMATH Open1380.81421arXiv1702.03163MaRDI QIDQ683231
Author name not available (Why is that?)
Publication date: 5 February 2018
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1702.03163
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