Show simple item record

dc.contributor.advisorGardi, Einan
dc.contributor.advisorPendleton, Brian
dc.contributor.authorSouto Gonçalves De Abreu, Samuel François
dc.date.accessioned2016-01-26T16:55:08Z
dc.date.available2016-01-26T16:55:08Z
dc.date.issued2015-11-26
dc.identifier.urihttp://hdl.handle.net/1842/14173
dc.description.abstractWe study the relations among unitarity cuts of a Feynman integral computed via diagrammatic cutting rules, the discontinuity across the corresponding branch cut, and the coproduct of the integral. For single unitarity cuts, these relations are familiar, and we show that they can be generalized to cuts in internal masses and sequences of cuts in different channels and/or internal masses. We develop techniques for computing the cuts of Feynman integrals in real kinematics. Using concrete one- and two-loop scalar integral examples we demonstrate that it is possible to reconstruct a Feynman integral from either single or double unitarity cuts. We then formulate a new set of complex kinematics cutting rules generalising the ones defined in real kinematics, which allows us to define and compute cuts of general one-loop graphs, with any number of cut propagators. With these rules, which are consistent with the complex kinematic cuts used in the framework of generalised unitarity, we can describe more of the analytic structure of Feynman diagrams. We use them to compute new results for maximal cuts of box diagrams with different mass configurations as well as the maximal cut of the massless pentagon. Finally, we construct a purely graphical coproduct of one-loop scalar Feynman diagrams. In this construction, the only ingredients are the diagram under consideration, the diagrams obtained by contracting some of its propagators, and the diagram itself with some of its propagators cut. Using our new definition of cut, we map the graphical coproduct to the coproduct acting on the functions Feynman diagrams and their cuts evaluate to. We finish by examining the consequences of the graphical coproduct in the study of discontinuities and differential equations of Feynman integrals.en
dc.contributor.sponsorotheren
dc.language.isoenen
dc.publisherThe University of Edinburghen
dc.relation.hasversionS. Abreu, R. Britto, C. Duhr, and E. Gardi, From multiple unitarity cuts to the coproduct of Feynman integrals, JHEP 1410 (2014) 125, [1401.3546].en
dc.relation.hasversionS. Abreu, MATHEMATICA package with results for diagrams and their cuts used in the check of the diagrammatic coproduct, 2015. http://www2.ph.ed.ac.uk/~s1039321/resultsOfDiagramsDiagCoprod.zip.en
dc.relation.hasversionSamuel Abreu, Ruth Britto, and Hanna Gronqvist. Cuts and coproducts of massive triangle diagrams, JHEP, 2015.en
dc.rightsAttribution-NonCommercial-ShareAlike 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/*
dc.subjectFeynmanen
dc.subjectFeynman diagramsen
dc.subjectHopf algebrasen
dc.titleCuts, discontinuities and the coproduct of Feynman diagramsen
dc.typeThesis or Dissertationen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD Doctor of Philosophyen


Files in this item

This item appears in the following Collection(s)

Show simple item record

Attribution-NonCommercial-ShareAlike 4.0 International
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-ShareAlike 4.0 International