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Cross-Order Integral Relations from Maximal Cuts

Johansson, Henrik and Kosower, David A. and Larsen, Kasper J. and Søgaard, Mads (2015) Cross-Order Integral Relations from Maximal Cuts. Physical Review D, 92 (2). Art. No. 025015. ISSN 0556-2821.

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We study the Anastasiou–Bern–Dixon–Kosower relation using maximal cuts of one- and two-loop integrals with up to five external legs. We show how to find a special combination of integrals that allows the relation to exist, and how to reconstruct the terms with one-loop integrals squared. The reconstruction relies on the observation that integrals across different loop orders can have support on the same generalized unitarity cuts and can share global poles. We discuss the appearance of nonhomologous integration contours in multivariate residues. Their origin can be understood in simple terms, and their existence enables us to distinguish contributions from different integrals. Our analysis suggests that maximal and near-maximal cuts can be used to infer the existence of integral identities more generally.

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Additional Information:This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Published by the American Physical Society. (Received 1 May 2015; published 10 July 2015) We have benefited from discussions with Simon Caron-Huot, David Skinner, Jaroslav Trnka, and Yang Zhang. K. J. L. is grateful for the hospitality of the Institute for Advanced Study in Princeton and the Institut de Physique Théorique, CEA Saclay, where part of this work was carried out. M. S. thanks SLAC National Accelerator Laboratory and the Institut de Physique Théorique, CEA-Saclay for hospitality during several phases of this project. H. J.’s work is supported in part by the Swedish Research Council under Grant No. 621–2014–5722, the Knut and Alice Wallenberg Foundation under Grant No. KAW 2013.0235 (Wallenberg Academy Fellowship), and the CERN-COFUND Fellowship program (cofunded via Marie Curie Actions Grant No. PCOFUND–GA–2010–267194 under the European Union’s Seventh Framework Programme). D. A. K.’s work has been supported by the European Research Council under Advanced Investigator Grant No. ERC–AdG–228301. D. A. K. also thanks the Moore Visiting Scholars program, the Moore Center for Theoretical Cosmology and Physics (under Grant No. 776), and the Walter Burke Institute for Theoretical Physics for their support. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under Grant Agreement No. 627521.
Group:Walter Burke Institute for Theoretical Physics, Moore Center for Theoretical Cosmology and Physics
Funding AgencyGrant Number
Swedish Research Council621–2014–5722
Knut and Alice Wallenberg FoundationKAW 2013.0235
Marie Curie ActionsPCOFUND–GA–2010–267194
European Research Council (ERC)ERC–AdG–228301
European Union Seventh Framework Programme627521
Gordon and Betty Moore Foundation776
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Record Number:CaltechAUTHORS:20150424-114953441
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56954
Deposited By: Joy Painter
Deposited On:24 Apr 2015 19:34
Last Modified:20 Nov 2018 21:42

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