From Loops to Trees By-passing Feynman's Theorem

By S. Catani, T. Gleisberg, F. Krauss, G. Rodrigo, J. Winter. 2008

188 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/02a536300ed73b92b5df69fb65b91944fdefa41b

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In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

In Nuclear and High Energy Physics

Citations in the corpus

One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts (2011, background): “As a final remark we note that other approaches to one-loop calculations beyond traditional Passarino-Veltman reduction and generalized unitarity have have been studied in the literature [33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], but we will not discuss them in this review.”
Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report (2017, methodology): “This problem can be overcome with the help of the loop-tree duality [423, 425, 427, 431, 433, 434]: A cyclicordered one-loop amplitude”
Loop amplitudes in gauge theories: modern analytic approaches (2010, methodology): “residue theorem for double cuts [48]; and a single-cut method has been found using the principles of Feynman’s Tree Theorem but grouping the terms together into a smaller set of single-cut amplitudes [44]. 5. D-dimensional unitarity We have seen how to evaluate four-dimensional cuts to solve for the”