Effective Field Theories from Soft Limits

TL;DR

This paper develops a method to derive scalar effective field theories from on-shell scattering amplitudes based on Lorentz invariance, factorization, and soft limit behavior, classifying theories by their soft properties and derivative order.

Contribution

It introduces a framework to construct and classify scalar EFTs directly from amplitude properties, linking soft limits to Lagrangian structures and identifying known theories within this scheme.

Findings

Derived EFTs from amplitude constraints including Nambu-Goldstone, DBI, and Galileons.

Classified scalar EFTs using derivative power counting and soft limit behavior.

Identified conditions where certain theories cannot exist due to inconsistency in amplitudes.

Abstract

We derive scalar effective field theories - Lagrangians, symmetries, and all - from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galileons. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.