Single-minus graviton tree amplitudes are nonzero

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.

12 pages, no figures. v2: minor edits