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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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Scattering amplitudes and toric geometry

TL;DR: In this paper, a toric geometric interpretation of scattering amplitudes is presented, where the singularities of the amplitudes are encoded in some subspaces of the toric variety, and this picture maps onto the Grassmannian description.
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MultivariateResidues: a Mathematica package for computing multivariate residues

TL;DR: This paper provides a Mathematica package for efficient evaluation of multivariate residues based on methods from computational algebraic geometry and shows that this evaluation can be non-trivial.
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Massive quark-gluon scattering amplitudes at tree level

TL;DR: In this paper, the results for four-, five-, and six-parton tree amplitudes for massive quark-antiquark scattering with gluons are calculated using the recursion relations of Britto, Cachazo, Feng, and Witten.
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Global Residues and Two-Loop Hepta-Cuts

TL;DR: In this article, the authors derived analytic expressions for coefficients of master integrals with two-loop crossed box topology in massless four-point amplitudes in any gauge theory, thereby providing additional steps towards automated computation of the full amplitude.
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Lotty – The loop-tree duality automation

TL;DR: The Mathematica package Lotty is introduced that automates the latter at multi-loop level and provides support to the all-loop causal representation recently conjectured by the same author.
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.
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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.
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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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