Constructing Amplitudes from Their Soft Limits
Camille Boucher-Veronneau, Andrew J. Larkoski
TL;DR
This work develops and systematizes inverse-soft as a method to construct tree-level scattering amplitudes from their soft limits, linking it to BCFW recursion. The authors show that, for both gauge theory and gravity, all tree-level amplitudes with up to seven external legs can be assembled from sequences of soft-factor insertions multiplied by lower-point amplitudes, and they identify NMHV gauge-theory amplitudes with certain helicity patterns that admit arbitrary numbers of legs. The approach hinges on precise momentum deformations (inverse-soft shifts) and a careful accounting of soft factors in gauge theory (unique) versus gravity (sum over terms). The results provide a new, soft-limit–driven pathway to obtain amplitudes, with potential extensions to higher points, supersymmetric theories, and loop-level structures.
Abstract
The existence of universal soft limits for gauge-theory and gravity amplitudes has been known for a long time. The properties of the soft limits have been exploited in numerous ways; in particular for relating an n-point amplitude to an (n-1)-point amplitude by removing a soft particle. Recently, a procedure called inverse soft was developed by which "soft" particles can be systematically added to an amplitude to construct a higher-point amplitude for generic kinematics. We review this procedure and relate it to Britto-Cachazo-Feng-Witten recursion. We show that all tree-level amplitudes in gauge theory and gravity up through seven points can be constructed in this way, as well as certain classes of NMHV gauge-theory amplitudes with any number of external legs. This provides us with a systematic procedure for constructing amplitudes solely from their soft limits.