New Formulas for Amplitudes from Higher-Dimensional Operators

Abstract

In this paper we study tree-level amplitudes from higher-dimensional operators, including $F^3$ operator of gauge theory, and $R^2$, $R^3$ operators of gravity, in the Cachazo-He-Yuan formulation. As a generalization of the reduced Pfaffian in Yang-Mills theory, we find a new, gauge-invariant object that leads to gluon amplitudes with a single insertion of $F^3$, and gravity amplitudes by Kawai-Lewellen-Tye relations. When reduced to four dimensions for given helicities, the new object vanishes for any solution of scattering equations on which the reduced Pfaffian is non-vanishing. This intriguing behavior in four dimensions explains the vanishing of graviton helicity amplitudes produced by the Gauss-Bonnet $R^2$ term, and provides a scattering-equation origin of the decomposition into self-dual and anti-self-dual parts for $F^3$ and $R^3$ amplitudes.

21 pages; v3: published version; a mistake in sec. 4.1 corrected

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• Inverse of the String Theory KLT Kernel
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• Shift symmetries, soft limits, and the double copy beyond leading order
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• On the New Factorizations of Yang-Mills Amplitudes
• Windings of twisted strings
• One-loop diagrams with quadratic propagators from the worldsheet
• A String Deformation of the Parke-Taylor Factor
• $\Delta$-Algebra and Scattering Amplitudes
• Bootstrapping solutions of scattering equations
• CHY formulae in 4d
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• UV consistency conditions for CHY integrands
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• CHY Theory for Several Fields
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