Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills

By R. Britto, F. Cachazo, Bo Feng. 2004

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Abstract One-loop amplitudes of gluons in N = 4 gauge theory can be written as linear combinations of known scalar box integrals with coefficients that are rational functions. In this paper we show how to use generalized unitarity to basically read off the coefficients. The generalized unitarity cuts we use are quadruple cuts. These can be directly applied to the computation of four-mass scalar integral coefficients, and we explicitly present results in next-to-next-to-MHV amplitudes. For scalar box functions with at least one massless external leg we show that by doing the computation in signature ( − − + + ) the coefficients can also be obtained from quadruple cuts, which are not useful in Minkowski signature. As examples, we reproduce the coefficients of some one-, two-, and three-mass scalar box integrals of the seven-gluon next-to-MHV amplitude, and we compute several classes of three-mass and two-mass-hard coefficients of next-to-MHV amplitudes to all multiplicities.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/cde5e221e90014e0b90a9c44e91aabb4af1e0658

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Citations in the corpus

Scattering amplitudes over finite fields and multivariate functional reconstruction (2016, neutral): “A(1, 2, 3, 4, 5) = i s 6 12 〈1 2〉〈2 3〉〈3 4〉〈4 5〉〈5 1〉 A(phase)(1−, 2, 3, 4, 5) = i (〈1 2〉 [23]〈3 1〉]) 2 s(3)12 〈1 2〉〈2 3〉〈3 4〉〈4 5〉〈5 1〉 A(phase)(1−, 2−, 3, 4, 5) = i 〈1 2〉 (4)s(4)12 〈1 2〉〈2 3〉〈3 4〉〈4 5〉〈5 1〉 , A(phase)(1−, 2, 3−, 4, 5) = i 〈1 3〉 (4)s(4)12 〈1 2〉〈2 3〉〈3 4〉〈4 5〉〈5 1〉 ,”
Color-kinematic duality for form factors (2012, background): “the integrand is indeed physical, one should check it against a complete set of (preferably D-dimensional) unitarity cuts [35, 38].”
Full one-loop amplitudes from tree amplitudes (2008, positive): “An important step in developing unitarity-based methods was made in [22] where it was shown that coefficients of four-point scalar integrals for multi-gluon processes can be calculated using quadruple cuts.”
On-the-fly reduction of open loops (2017, background): “, the cutting rule should guarantee that the position of the cut and its direction remain unchanged after a pinch. More explicitly, the desired cut conﬁgurations after a D¯ j pinch with j>0 are I N[1] = {S 1 ⊕S 2,S 3,...,S N}, (99) I N[j] = {S 1,...,S j−1,S j⊕S j+1,S j+2,...,S N} for 2 ≤j≤N−2, (1”
Integrand reduction of one-loop scattering amplitudes through Laurent series expansion (2012, background): “ering amplitudes has been highly stimulated by a deeper understanding of their multi-channel factorization properties under special kinematics enforced by on-shellness [1,2] and generalized unitarity [3,4]. Analyticity and unitarity of scattering amplitudes have then been strengthened by the complem”
A Note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix (2008, methodology): “ − g ,3 + f ,4 + g ). Proceeding as before, the fermionic integrations produce a factor of h51i3hPˆ1ihPˆˆ2i3hˆ23 i. Standard manipulations lead to h1Pˆihˆ2Pˆi = h15i[52]/(h34i[34], hˆ23 i = −[45]h34i/[25], and one quickly ﬁnds that A(5 − f ,1g ,2 − g ,3 + f ,4 + g ) = i [34]3[45] [12][23][34][45][51”
One-loop amplitudes of gluons in supersymmetric QCD (2005, methodology): “next-to-MHV six-gluon amplitudes were computed using quadruple cuts [ 5 ].”
Taming tree amplitudes in general relativity (2007, background): “f gluons. More recently, a new set of recursion relations for tree level amplitudes of gluons was introduced by Britto, Feng and the third author [7]. These recursion relations were inspired { 1 { by [8, 9] and reproduced very compact results obtained in [10] by studying the IR behavior of N= 4 one-”