New formulas for amplitudes from higher-dimensional operators

Abstract

In this paper we study tree-level amplitudes from higher-dimensional operators, including F3 operator of gauge theory, and R2, R3 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 F3, 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 R2 term, and provides a scattering-equation origin of the decomposition into self-dual and anti-self-dual parts for F3 and R3 amplitudes.