On-Shell Recursion Relations for Nonrelativistic Effective Field Theories

TL;DR

This paper develops on-shell recursion relations for nonrelativistic EFTs with enhanced soft limits, enabling systematic calculation of scattering amplitudes and constraining the EFT landscape using soft theorems.

Contribution

It introduces the first on-shell recursion relations tailored for nonrelativistic EFTs with enhanced soft limits, expanding tools for amplitude calculations in these theories.

Findings

Recursion relations derived for nonrelativistic EFTs.

Analytic calculation of tree-level amplitudes demonstrated.

Soft theorems constrain the EFT landscape similarly to relativistic cases.

Abstract

We derive on-shell recursion relations for nonrelativistic effective field theories (EFTs) with enhanced soft limits. The recursion relations are illustrated through analytic calculation of tree-level scattering amplitudes in theories with a complex Schr\"odinger-type field, real scalar with linear dispersion relation, and real scalar with Lifshitz-type dispersion relation. Our results show that the landscape of gapless nonrelativistic EFTs with local $S$-matrix can be constrained by soft theorems and the consistency of the low-energy $S$-matrix similarly to massless relativistic EFTs.