On-shell recursion relations for nonrelativistic effective field theories

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 Schrodinger-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. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

In this study, on-shell recursion relations for nonrelativistic effective field theories with enhanced soft limits are derived, and illustrated through analytic calculations of tree-level scattering amplitudes. The results suggest 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, similar to massless relativistic EFTs.