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One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits

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TLDR
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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Generalized unitarity and six-dimensional helicity

TL;DR: In this paper, the unitarity method was combined with the six-dimensional helicity formalism of Cheung and O'Connell to construct loop-level scattering amplitudes for the Higgs infrared regulator.
Journal ArticleDOI

FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs

TL;DR: FiniteFlow as discussed by the authors is a framework for defining and executing numerical algorithms over finite fields and reconstructing multivariate rational functions, which allows to easily implement a wide range of methods in high-level languages and computer algebra systems, without being concerned with the low-level details of the numerical implementation.
Journal ArticleDOI

Computing one-loop amplitudes from the holomorphic anomaly of unitarity cuts

TL;DR: In this paper, a systematic way to carry out the method introduced in F. Cachazo, hep-th/0410077 for computing certain unitarity cuts of one-loop amplitudes of gluons was proposed.
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Optimizing the Reduction of One-Loop Amplitudes

TL;DR: In this paper, an optimization of the reduction algorithm of one-loop amplitudes in terms of master integrals is presented based on the exploitation of the polynomial structure of the integrand when evaluated at values of the loopmomentum fulfilling multiple cut-conditions, as emerged in the OPP-method.
Journal ArticleDOI

Dual identities inside the gluon and the graviton scattering amplitudes

TL;DR: In this paper, the properties of the open string tree and the M-gluon tree were used to derive dual identities inside the tree, which can be carried over to loop amplitudes using the unitarity method.
References
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Journal ArticleDOI

Amplitude for n-gluon scattering.

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.
Journal ArticleDOI

On analytic properties of vertex parts in quantum field theory

L.D. Landau
- 01 Oct 1959 - 
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.
Journal ArticleDOI

One-loop corrections to five-gluon amplitudes.

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.
Journal ArticleDOI

Efficient calculation of one-loop QCD amplitudes

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.
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