Probing Scalar Effective Field Theories with the Soft Limits of Scattering Amplitudes

TL;DR

This paper explores the soft limits of scalar effective field theories with multiple derivative power counting parameters, extending on-shell recursion techniques to identify unique symmetries like DBI and special galileons.

Contribution

It clarifies enhanced soft limits in scalar EFTs with multiple parameters and demonstrates how these limits uniquely identify DBI and special galileon theories using on-shell methods.

Findings

Enhanced soft limits characterize DBI and galileon symmetries.

Recursion techniques successfully generate six-point amplitudes.

Amplitudes exhibit invariance under DBI galileon duality.

Abstract

We investigate the soft behaviour of scalar effective field theories (EFTs) when there is a number of distinct derivative power counting parameters, $\rho_1< \rho_2<\ldots < \rho_Q$. We clarify the notion of an enhanced soft limit and use these to extend the scope of on-shell recursion techniques for scalar EFTs. As an example, we perform a detailed study of theories with two power counting parameters, $\rho_1=1$ and $\rho_2=2$, that include the shift symmetric generalised galileons. We demonstrate that the minimally enhanced soft limit uniquely picks out the Dirac-Born-Infeld (DBI) symmetry, including DBI galileons. For the exceptional soft limit we uniquely pick out the special galileon within the class of theories under investigation. We study the DBI galileon amplitudes more closely, verifying the validity of the recursion techniques in generating the six point amplitude, and explicitly demonstrating the invariance of all amplitudes under DBI galileon duality.