One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
TL;DR: In this paper, the authors presented a technique which utilizes unitarity and collinear limits to construct ansatze for one-loop amplitudes in gauge theory, and proved that their $N=4$ ansatz is correct using general properties of the relevant one-loops $n$-point integrals.
Abstract: We present a technique which utilizes unitarity and collinear limits to construct ansatze for one-loop amplitudes in gauge theory. As an example, we obtain the one-loop contribution to amplitudes for $n$ gluon scattering in $N=4$ supersymmetric Yang-Mills theory with the helicity configuration of the Parke-Taylor tree amplitudes. We prove that our $N=4$ ansatz is correct using general properties of the relevant one-loop $n$-point integrals. We also give the ``splitting amplitudes'' which govern the collinear behavior of one-loop helicity amplitudes in gauge theories.
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TL;DR: MadGraph5 aMC@NLO as discussed by the authors is a computer program capable of handling all these computations, including parton-level fixed order, shower-matched, merged, in a unified framework whose defining features are flexibility, high level of parallelisation and human intervention limited to input physics quantities.
Abstract: We discuss the theoretical bases that underpin the automation of the computations of tree-level and next-to-leading order cross sections, of their matching to parton shower simulations, and of the merging of matched samples that differ by light-parton multiplicities. We present a computer program, MadGraph5 aMC@NLO, capable of handling all these computations — parton-level fixed order, shower-matched, merged — in a unified framework whose defining features are flexibility, high level of parallelisation, and human intervention limited to input physics quantities. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the LHC and to a 1-TeV e + e − collider. While next-to-leading order results are restricted to QCD corrections to SM processes in the first public version, we show that from the user viewpoint no changes have to be expected in the case of corrections due to any given renormalisable Lagrangian, and that the implementation of these are well under way.
6,509 citations
TL;DR: In this paper, Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves, which is a consequence of an equivalence between the perturbative expansion of = 4 super Yang-Mills theory and the D-instanton expansion of a certain string theory.
Abstract: Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of = 4 super Yang-Mills theory and the D-instanton expansion of a certain string theory, namely the topological B model whose target space is the Calabi-Yau supermanifold
1,626 citations
TL;DR: In this article, the authors presented new recursion relations for tree amplitudes in gauge theory that give very compact formulas, in which all particles are on-shell and momentum conservation is preserved.
1,267 citations
TL;DR: In this paper, a large class of one-loop amplitudes for massless particles that can be constructed via unitarity from tree amplitudes, without any ambiguities, is identified.
1,164 citations
TL;DR: In this paper, the leading-color (planar) three-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 - 2 -epsilon dimensions was constructed via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already.
Abstract: We compute the leading-color (planar) three-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 - 2{epsilon} dimensions, as a Laurent expansion about {epsilon} = 0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N = 4 amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated ansatz for the maximally helicity-violating n-point amplitudes to all loop orders. The 1/{epsilon}{sup 2} pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.
1,071 citations
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TL;DR: A nontrivial squared helicity amplitude is given for the scattering of an arbitrary number of gluons to lowest order in the coupling constant and to leading order inThe number of colors.
Abstract: A nontrivial squared helicity amplitude is given for the scattering of an arbitrary number of gluons to lowest order in the coupling constant and to leading order in the number of colors.
963 citations
TL;DR: In this paper, a general method of finding the singularities of quantum field theory values on the basis of graph techniques is described, and a graph-based approach is used to find the singularity of quantum fields.
656 citations
385 citations
TL;DR: This work presents the one-loop helicity amplitudes with five external gluons, a computation that employs string-based methods, new techniques for performing tensor integrals, and improvements in the spinor helicity method.
Abstract: We present the one-loop helicity amplitudes with five external gluons. The computation employs string-based methods, new techniques for performing tensor integrals, and improvements in the spinor helicity method.
343 citations
TL;DR: The outline of a new and efficient technique for the calculation of loop amplitudes in a gauge theory based on the technology of four-dimensional heterotic strings is presented, which finds complete agreement with the previous Feynman-diagram calculation of Ellis and Sexton.
Abstract: We present the outline of a new and efficient technique for the calculation of loop amplitudes in a gauge theory. The technique is based on the technology of four-dimensional heterotic strings. We display here the application to the calculation of the one-loop corrections to gluon-gluon scattering, in ordinary dimensional regularization. We find complete agreement with the previous Feynman-diagram calculation of Ellis and Sexton.
238 citations