From Multileg Loops to Trees (by-passing Feynman's Tree Theorem)

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We illustrate a duality relation between one-loop integrals and single-cut phase-space integrals. The duality relation is realised by a modification of the customary +i0 prescription of the Feynman propagators. The new prescription regularizing the propagators, which we write in a Lorentz covariant form, compensates for the absence of multiple-cut contributions that appear in the Feynman Tree Theorem. The duality relation can be extended to generic one-loop quantities, such as Green's functions, in any relativistic, local and unitary field theories. The physics program of LHC requires the evaluation of multi-leg signal and background processes at next-to-leading order (NLO). In the recent ... continued below

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6 pages

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Rodrigo, German; Catani, Stefano; Gleisberg, Tanju; Krauss, Frank & Winter, Jan-Christopher October 14, 2011.

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We illustrate a duality relation between one-loop integrals and single-cut phase-space integrals. The duality relation is realised by a modification of the customary +i0 prescription of the Feynman propagators. The new prescription regularizing the propagators, which we write in a Lorentz covariant form, compensates for the absence of multiple-cut contributions that appear in the Feynman Tree Theorem. The duality relation can be extended to generic one-loop quantities, such as Green's functions, in any relativistic, local and unitary field theories. The physics program of LHC requires the evaluation of multi-leg signal and background processes at next-to-leading order (NLO). In the recent years, important efforts have been devoted to the calculation of many 2 {yields} 3 processes and some 2 {yields} 4 processes. We have recently proposed a method to compute multi-leg one-loop cross sections in perturbative field theories. The method uses combined analytical and numerical techniques. The starting point of the method is a duality relation between one-loop integrals and phase-space integrals. In this respect, the duality relation has analogies with the Feynman's Tree Theorem (FTT). The key difference with the FTT is that the duality relation involves only single cuts of the one-loop Feynman diagrams. In this talk, we illustrate the duality relation, and discuss its correspondence, similarities, and differences with the FTT.

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6 pages

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  • Journal Name: Nucl.Phys.Proc.Suppl.183:262-267,2008; Conference: To appear in the proceedings of 9th Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory, Sondershausen, Germany, 20-25 Apr 2008

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  • Report No.: SLAC-PUB-14635
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 1027217
  • Archival Resource Key: ark:/67531/metadc846443

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  • October 14, 2011

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  • May 19, 2016, 3:16 p.m.

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  • Aug. 16, 2017, 11:47 a.m.

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Rodrigo, German; Catani, Stefano; Gleisberg, Tanju; Krauss, Frank & Winter, Jan-Christopher. From Multileg Loops to Trees (by-passing Feynman's Tree Theorem), article, October 14, 2011; United States. (digital.library.unt.edu/ark:/67531/metadc846443/: accessed August 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.