Pfaffian Diagrams for Gluon Tree Amplitudes

Abstract

Pfaffian diagrams are formulated to represent gluon amplitudes computed from the Cachazo-He-Yuan (CHY) formula. They may be regarded as a systematic regrouping of Feynman diagrams after internal momenta are expanded and products of vertex factors are evaluated. This reprocessing enables gluon amplitudes expressed in Pfaffian diagrams to contain less terms. For example, there are 19 terms for the four-point amplitude in Pfaffian diagrams, and 35 terms in Feynman diagrams. Gauge invariance is simpler and more explicit in Pfaffian diagrams, in that subset of diagrams with the same root configuration are already gauge invariant in all lines but two. In getting to these results, several technical difficulties must be overcome. Double poles must be converted to simple poles, integrations must be carried out directly and formulated into simple rules, and the three \M constant lines must be suitably chosen to minimize the number of terms present.

References in corpus (17)

• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Scattering Equations and KLT Orthogonality
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Proof of the Formula of Cachazo, He and Yuan for Yang-Mills Tree Amplitudes in Arbitrary Dimension
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• BCJ numerators from reduced Pfaffian
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Scattering Equations and Feynman Diagrams
• Integration Rules for Scattering Equations
• Computation of Contour Integrals on ${\mathcal{M}}_{0,n}$
• Evaluation of the CHY Gauge Amplitude
• Labelled tree graphs, Feynman diagrams and disk integrals
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• The Role of Möbius Constants and Scattering Functions in CHY Scalar Amplitudes
• CHY formulae in 4d

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• Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory
• Off-Shell Yang-Mills Amplitude in the CHY Formalism
• UV consistency conditions for CHY integrands
• CHY Theory for Several Fields
• Color-Kinematics Relation from the Feynman Diagram Perspective