The Twelve-Graviton Next-to-MHV Amplitude from Risager's Construction

TL;DR

This paper derives the explicit form of the residue at infinity for the 12-graviton NMHV amplitude, completing the first full CSW-like analytic expression for this amplitude using Risager's construction.

Contribution

It provides the explicit analytic form of the residue at infinity for the 12-graviton NMHV amplitude, extending Risager's method to gravity.

Findings

Explicit residue at infinity for 12-graviton NMHV amplitude obtained.

First full CSW-like analytic expression for twelve-graviton NMHV amplitude.

Method applicable to higher-point amplitudes.

Abstract

The MHV or CSW expansion of tree-level Yang-Mills amplitudes provides an elegant and simple way of obtaining analytic formulas for S-matrix elements. Inspired by the BCFW technique, a systematic approach to obtain the MHV expansion was introduced by Risager, using a particular complex deformation. Although it works for Yang-Mills amplitudes, Risager's technique fails to provide an MHV expansion already for Next-to-MHV gravity amplitudes with more than eleven particles, as shown by Bianchi, Elvang and Freedman in 2008. This fact implies that in this sector there is a contribution at infinity starting at n = 12. In this note we determine the explicit analytic form of this residue at infinity for n = 12. Together with the terms of the Risager MHV expansion, the residue at infinity completes the first full CSW-like analytic expression of the twelve-graviton NMHV amplitude. Our technique can also be used to compute the residue at infinity for higher points.