A Tree-Loop Duality Relation at Two Loops and Beyond

Abstract

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.

20 pages. Few typos corrected, some additional comments included, Appendix B and one reference added. Final version as published in JHEP

References in corpus (11)

• Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO
• Higgs production via vector-boson fusion at NNLO in QCD
• Assault on the NLO Wishlist: pp -> tt bb
• Precise Predictions for W + 3 Jet Production at Hadron Colliders
• NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. full hadronic results
• Electroweak corrections to W + jet hadroproduction including leptonic W-boson decays
• From loops to trees by-passing Feynman's theorem
• Electroweak corrections to hadronic production of W bosons at large transverse momenta
• NNLO QCD predictions for the H -> WW -> l l nu nu signal at the LHC
• W boson production at hadron colliders: the lepton charge asymmetry in NNLO QCD
• QCD Calculations by Numerical Integration

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