{"paper":{"title":"Theoretical foundations and applications of the Loop-Tree Duality in Quantum Field Theories","arxiv_id":"1509.07167","primary_cat":"hep-ph","submitted_at":"2015-09-23T22:05:19+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. 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loop-energy-integration.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.16,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.9,"result":0.0,"background":0.1,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.7,"id":"s2","own":false,"role":"method","text":"The result is a sum over all possible single cuts of the Feynman diagram in consideration integrated over a modified phase space.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.19,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.7,"result":0.2,"background":0.1,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.8,"id":"s3","own":false,"role":"interpretation","text":"These single-cut integrals, called Dual contributions, are in fact tree-level objects and thus give rise to the opportunity of bringing loop- and tree-contributions together, treating them simultaneously in a common Monte Carlo event generator.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.16,"main_claim_p":0.14,"quantitative":false,"quantitative_p":0.12,"role_probabilities":{"gap":0.0,"method":0.04,"result":0.02,"background":0.13,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.8}},{"i":4,"p":1.0,"id":"s4","own":false,"role":"background","text":"Initially introduced for one-loop scalar integrals, the applicability of the LTD has been expanded ever since.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.06,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.15,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":5,"p":0.81,"id":"s5","own":true,"role":"contribution","text":"In this thesis, we show how to deal with Feynman graphs beyond simple poles by taking advantage of Integration By Parts (IBP) 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