Eliminating spurious poles from gauge-theoretic amplitudes

By A. Hodges. 2009

521 citations recorded by the source corpus.

A bstractThis note addresses the problem of spurious poles in gauge-theoretic scattering amplitudes. New twistor coordinates for the momenta are introduced, based on the concept of dual conformal invariance. The cancellation of spurious poles for a class of NMHV amplitudes is greatly simplified in these coordinates. The poles are eliminated altogether by defining a new type of twistor integral, dual to twistor diagrams as previously studied, and considerably simpler. The geometric features indicate a supersymmetric extension of the formalism at least to all NMHV amplitudes, allowing the dihedral symmetry of the super-amplitude to be made manifest. More generally, the definition of ‘momentum-twistor’ coordinates suggests a powerful new approach to the study of scattering amplitudes.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1ccfb5a661734a0f491299f279041abe1a80d6e6

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In Nuclear and High Energy Physics

1. S. Caron-Huot
2. L. Dixon
3. N. Arkani-Hamed
4. J. Drummond
5. F. Cachazo
6. P. Vieira
7. A. Sever
8. M. Hippel

Citations in the corpus

• Bootstrapping an NMHV amplitude through three loops (2014, methodology): “Using the coordinates (xi, θi) we may define momentum (super)twistors [67, 68]”
• Classical polylogarithms for amplitudes and Wilson loops. (2010, background): “) We anticipate that for general n the best variables for studying the remainder function will be the momentum twistors of [17].”
• TASI Lectures on Scattering Amplitudes (2017, methodology): “From the top line, we deduce that if 〈12〉 6 = 0, then [12] = 0.”
• Scattering Amplitudes and the Positive Grassmannian (2012, methodology): “18) where we have introduced the super momentum-twistors Z, [127], according to:”
• Cluster algebras (2014, unknown): “This insight combined with an idea of Hodges [29] led Arkani-Hamed and Trnka to introduce the amplituhedron [7] , defined as the image of the positive Grassmannian under the ampli-tuhedron map .”
• A two-loop five-gluon helicity amplitude in QCD (2013, methodology): “!2 kinematics. In this paper, we use the momentum twistor parametrization for the analytical computations, in which the kinematics can be represented by momentum twistors Zi(i;~i) for each momentum [60]. The advantage of momentum twistor variables is that all identities like the Schouten identity, e”
• A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon (2014, background): “We describe the space as kinematical because the n points Zi (known as momentum twistors [79]) in P 3 define, after choosing a preferred bitwistor I ∈ P3 ∧ P3, a light-like polygonal contour in Minkowski space-time via”
• Local integrals for planar scattering amplitudes (2010, methodology): “Its our please to acknowledge stimulating discussions with Simon Caron-Huot, James Drummond, Johannes Henn, Andrew Hodges, Lionel Mason, and Dave Skinner.”
• The four-loop six-gluon NMHV ratio function (2015, background): “The NMHV ratio function can be further decomposed into two independent functions, V and Ṽ , which multiply dual superconformal R-invariants — five-brackets of supersymmetric versions of momentum twistors [24, 25].”
• Unification of residues and Grassmannian dualities (2009, background): “These are the objects introduced by Hodges [5] in order to make dual-superconformal invariance [6–9] manifest.”
• The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM (2010, background): “It is likely that a deeper understanding of the contours associated with the “Hodges diagrams” [70,77], already for twistor-space tree-amplitudes in (3, 1)-signature, will be important to make progress here.”
• Scattering forms and the positive geometry of kinematics, color and the worldsheet (2017, background): “In contrast, this new representation comes from a simple triangulation that keeps this symmetry manifest, much as “BCFW triangulations” of the amplituhedron [10, 11] make manifest the dual conformal/Yangian symmetries of planar N = 4 SYM that are not seen in the usual Feynman diagram expansion.”
• The Grassmannian origin of dual superconformal invariance (2009, methodology): “As we will see this linear transformation takes us from the momentum variables to the “momentum twistor” variables recently introduced in a remarkable paper by Hodges [ 5 ].”