Constructing Amplitudes from Their Soft Limits

TL;DR

This paper reviews a systematic method to construct gauge theory and gravity amplitudes from their soft limits, extending to seven points and certain NMHV amplitudes, linking soft limits with recursive construction techniques.

Contribution

It introduces and relates the inverse soft procedure to BCFW recursion, enabling construction of tree-level amplitudes from soft limits for various cases.

Findings

All tree-level amplitudes up to seven points can be constructed via inverse soft.

Certain NMHV amplitudes with any number of legs are also constructible.

The method provides a systematic way to build amplitudes solely from soft limits.

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.