A tree-loop duality relation at two loops and beyond
By I. Bierenbaum, S. Catani, P. Draggiotis, G. Rodrigo. 2010
134 citations recorded by the source corpus.
The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops. The duality relation is realized by a modification of the customary + i0 prescription of the Feynman propagators, which compensates for the absence of the multiple-cut contributions that appear in the Feynman tree theorem. We rederive the duality theorem at one-loop order in a form that is more suitable for its iterative extension to higher-loop orders. We explicitly show its application to two-and three-loop scalar master integrals, and we discuss the structure of the occurring cuts and the ensuing results in detail.
Subfields: Applied Mathematics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/0b298c97773072496059e8cb63d9227b4c5c23af
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In Applied Mathematics
- Gudrun Heinrich
- Stefano Pozzorini
- M. Schönherr
- Stefan Kallweit
- Thomas Gehrmann
- J. Lindert
- Stefan Weinzierl
- G. Luisoni
In Nuclear and High Energy Physics
- Atlas Collaboration
- Cms Collaboration
- Gudrun Heinrich
- M. Schönherr
- Ansgar Denner
- Stefan Dittmaier
- A. Larkoski
- S. Höche
Citations in the corpus
- Loop amplitudes in gauge theories: modern analytic approaches (2010, background): “The operations that have been proposed to construct one-loop amplitudes from their single cuts using different propagator prescriptions [43, 44] can be extended to higher-loop integrals [45], since there is no need for a basis of master integrals, and”
- Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report (2017, methodology): “The LTD representation of the two-loop scattering amplitude is obtained by setting two internal lines on-shell [424], whilst the squared one-loop introduces two independent loop three-momenta.”
- One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts (2011, background): “Second, in this review we did not talk about attempts to design a framework where one-loop computations can be performed by pure numerical methods [33, 34, 35, 36, 37, 38, 39, 40, 44, 41, 42, 43, 44, 139].”