Single-minus graviton tree amplitudes are nonzero

TL;DR

This paper demonstrates that single-minus graviton tree amplitudes, previously thought to vanish, are actually nonzero under certain conditions, and provides recursive formulas and symmetry-based insights into their structure.

Contribution

It introduces a new understanding of single-minus graviton amplitudes, deriving a Berends-Giele recursion and linking the amplitudes to a recursive Ward identity.

Findings

Single-minus amplitudes are nonzero in specific configurations.

Derived a Berends-Giele recursion relation for these amplitudes.

Connected the amplitudes to an $ ext{w}_{1+ ext{infinity}}$ Ward identity.

Abstract

Single-minus tree-level $n$-graviton scattering amplitudes are revisited. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. A Berends-Giele recursion relation for these amplitudes is derived and solved in a form involving a sum over trees. In a restricted kinematic decay region, this solution simplifies significantly to an $(n{-}2)$-fold product of soft factors. It is further shown in this region that, combined with suitable analyticity assumptions, the $n$-graviton amplitude is generated by a recursive $\mathcal{L}w_{1+\infty}$ Ward identity with the three-graviton amplitude as a seed.