On-shell recurrence relations for one-loop QCD amplitudes

By Z. Bern, L. Dixon, David A. Kosower. 2005

201 citations recorded by the source corpus.

We present examples of on-shell recurrence relations for determining rational functions appearing in one-loop QCD amplitudes. In particular, we give relations for one-loop QCD amplitudes with all legs of positive helicity, or with one leg of negative helicity and the rest of positive helicity. Our recurrence relations are similar to the tree-level ones described by Britto, Cachazo, Feng and Witten. A number of new features arise for loop amplitudes in non-supersymmetric theories like QCD, including boundary terms and double poles. We show how to eliminate the boundary terms, which would interfere with obtaining useful relations. Using the relations we give compact explicit expressions for the n-gluon amplitudes with one negative-helicity gluon, up through n = 7.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8ba822ffe7f634d6b0b54ea68e293446678efb9f

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In Nuclear and High Energy Physics

Citations in the corpus

A direct proof of the CSW rules (2005, methodology): “The methods of BCFW recursion have been applied and extended with great success to both tree-level calculations in Yang–Mills and other theories [41, 42, 43, 44, 45, 46, 47, 48] as well as one-loop calculations [49, 50, 51, 52], and, in some of these cases, been merged with technology such as unitar”
Tree level recursion relations in general relativity (2005, unknown): “1 This iteration procedure was used recently in [18] to find recursion relations for all plus one-loop amplitudes of gluons.”
Taming tree amplitudes in general relativity (2007, methodology): “This was actually the motivation for the first use of compositions in the literature in [37].”
Cut-constructible part of QCD amplitudes (2006, background): “ rational function, and tackle these two pieces separately. The reason is as follows. Due to a better understanding of the recursive structure of QCD amplitudes, at tree level [35,36] and at one-loop [56], and exploiting the knowledge of their collinear and soft-behaviour, it has recently been shown”
Extensions of theories from soft limits (2016, background): “This deformation can be thought of as a composition of two BCFW deformations [21, 23].”
A recursion relation for gravity amplitudes (2005, unknown): “♣{j.a.p.bedford, a.brandhuber, w.j.spence, g.travaglini}@qmul.ac.uk”
Loop corrections to soft theorems in gauge theories and gravity (2014, background): “Since such contributions are ubiquitous for recursions of rational terms in gauge theories [43], we strongly suspect that corrections for S (1) YM is needed there as well.”