2024/05/01 by Cachazo, Freddy, Leon, Pablo
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2405.00660
In this note we study tree-level scattering amplitudes of gravitons under a natural deformation which in the large z limit can be interpreted either as a k-hard-particle limit or as a (n-k)-soft-particle limit. When k=2 this becomes the standard BCFW deformation while for k=3 it leads to the Risager deformation. The hard- to soft-limit map we define motivates a way of computing the leading order behavior of amplitudes for large z directly from soft limits. We check the proposal by applying the k=3 and k=4 versions to NMHV and N2MHV gravity amplitudes respectively. The former reproduces in a few lines the result recently obtained by using CHY-like techniques in \citeBCL. The N2MHV formula is also remarkably simple and we give support for it using a CHY-like computation. In the k=2 case applied to any gravity amplitude, the multiple soft-limit analysis reproduces the correct \cal O(z-2) behavior while explicitly showing the source of the mysterious cancellation among Feynman diagrams that tames the behavior from the \cal O(zn-5) of individual Feynman diagrams down to the \cal O(z-2) of the amplitude.