Cross-Order Integral Relations from Maximal Cuts

Henrik Johansson (1, 2, 3) , David A. Kosower (4, 5) , Kasper J. Larsen (6, 7) , Mads Sogaard (8)

1 cern - CERN, Theory Division
2 Department of Physics and Astronomy [Uppsala]
3 Department of Physics [Stockholm]
4 CALTECH - California Institute of Technology
5 IPHT - Institut de Physique Théorique - UMR CNRS 3681
6 NIKHEF - National Institute for Subatomic Physics [Amsterdam]
7 ITP - Institute for Theoretical Physics [ETH Zürich]
8 NBI - Niels Bohr Institute [Copenhagen]

We study the ABDK 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.

Domains: High Energy Physics - Theory [hep-th]

Henrik Johansson, David A. Kosower, Kasper J. Larsen, Mads Sogaard. Cross-Order Integral Relations from Maximal Cuts. Biophysical Reviews and Letters, 2015, 92, pp.025015 ⟨10.1103/PhysRevD.92.025015⟩. ⟨cea-01297652⟩