On-shell recursion relations for nonrelativistic effective field theories

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 Schrödinger-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.