From loops to trees by-passing Feynman's theorem

We derive a duality relation between one-loop integrals and phase-space integrals emerging from them through single cuts. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators. The new prescription regularizing the propagators, which we write...

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Bibliographic Details
Published in:arXiv.org 2008-09
Main Authors: Catani, Stefano, Gleisberg, Tanju, Krauss, Frank, German, Rodrigo, Jan-Christopher Winter
Format: Article
Language:English
Subjects:
Amplitudes
Cross-sections
Green's functions
Integrals
Mathematical analysis
Scattering
Theorems
Online Access:Get full text
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Summary:We derive a duality relation between one-loop integrals and phase-space integrals emerging from them through single cuts. The duality relation is realized 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 applied to generic one-loop quantities in any relativistic, local and unitary field theories. %It is suitable for applications to the analytical calculation of %one-loop scattering amplitudes, and to the numerical evaluation of %cross-sections at next-to-leading order. We discuss in detail the duality that relates one-loop and tree-level Green's functions. We comment on applications to the analytical calculation of one-loop scattering amplitudes, and to the numerical evaluation of cross-sections at next-to-leading order.
ISSN:2331-8422
DOI:10.48550/arxiv.0804.3170