On-Shell Recursion Relations for Effective Field Theories

TL;DR

This work extends on-shell recursion to effective field theories by introducing a rescaling momentum shift and a soft-behavior encoded factor to cancel soft zeros, enabling contour-based recursion using only factorization data. By linking large-z scaling to the soft degree σ and a derivative-counting parameter ρ, it provides a clear criterion (and a classification) for when EFT amplitudes are on-shell constructible, including exceptional theories with enhanced soft limits. The authors apply the construction to the non-linear sigma model, Dirac-Born-Infeld theory, and Galileons, deriving explicit recursion relations and showing that higher-point amplitudes can be built from lower-point seeds with results coinciding with traditional Feynman-diagram expectations. The framework not only unifies EFT recursion under soft constraints but also suggests deeper connections to scattering-equation formalisms and potential bonus relations in exceptional theories.

Abstract

We derive the first ever on-shell recursion relations for amplitudes in effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in theories like the non- linear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible.