From loops to trees by-passing Feynman's theorem
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.
Cite
@article{arxiv.0804.3170,
title = {From loops to trees by-passing Feynman's theorem},
author = {Stefano Catani and Tanju Gleisberg and Frank Krauss and German Rodrigo and Jan-Christopher Winter},
journal= {arXiv preprint arXiv:0804.3170},
year = {2009}
}
Comments
46 pages. A new appendix included. Appendix B simplified. Some comments and references added. Final version published in JHEP