From Multileg Loops to Trees (by-passing Feynman's Tree Theorem) [electronic resource].

Published:: Washington, D.C. : United States. Dept. of Energy, 2011.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
Physical Description:: 6 pages : digital, PDF file
Additional Creators:: SLAC National Accelerator Laboratory, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information

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Summary:

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 → 3 processes and some 2 → 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.

Report Numbers:

E 1.99:slac-pub-14635
slac-pub-14635

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Note:

Published through SciTech Connect.
10/14/2011.
"slac-pub-14635"
"arXiv:0807.0531"
Nucl.Phys.Proc.Suppl.183:262-267,2008
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.
Catani, Stefano; Krauss, Frank; Gleisberg, Tanju; Rodrigo, German; Winter, Jan-Christopher.

Funding Information:

AC02-76SF00515

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