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arXiv · 0804.3170

From loops to trees by-passing Feynman's theorem

Stefano Catani·Tanju Gleisberg·Frank Krauss·German Rodrigo·Jan-Christopher Winter
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Abstract

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.

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Stefano Catani, Tanju Gleisberg, Frank Krauss, German Rodrigo, Jan-Christopher Winter. 2008-09-11. From loops to trees by-passing Feynman's theorem. https://doi.org/10.1088/1126-6708%2F2008%2F09%2F065

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