New Formulas for Amplitudes from Higher-Dimensional Operators

TL;DR

This paper introduces new formulas for computing tree-level amplitudes involving higher-dimensional operators in gauge theory and gravity, revealing their behavior in four dimensions and explaining amplitude vanishing phenomena.

Contribution

It generalizes the reduced Pfaffian in Yang-Mills theory to include higher-dimensional operators, providing new gauge-invariant objects for amplitude calculations.

Findings

New gauge-invariant objects for $F^3$ and $R^3$ amplitudes

Explanation for vanishing graviton amplitudes with $R^2$ terms

Scattering-equation origin of self-dual and anti-self-dual decomposition

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.