Recursion relations from soft theorems

TL;DR

This paper introduces new on-shell recursion relations for scattering amplitudes that satisfy soft theorems, broadening the scope of recursive techniques to include theories with non-vanishing soft limits and applying them to various models.

Contribution

It generalizes existing recursion relations to include amplitudes with non-vanishing soft limits, enabling calculations in a wider class of theories.

Findings

Recursion relations applicable to amplitudes with soft theorems.

Successful application to tree-level amplitudes in multiple theories.

Extension of previous methods to non-vanishing soft limits.

Abstract

We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large-z behaviour. This work is a generalization of the recursion relations recently obtained by Cheung et al for amplitudes in scalar effective field theories with enhanced vanishing soft behaviours, which can be regarded as a special case of those with non-vanishing soft limits. We apply the recursion relations to tree-level amplitudes in various theories, including amplitudes in the Akulov-Volkov theory, amplitudes containing dilatons of spontaneously-broken conformal symmetry.