On the Inverse Problem in Effective Field Theory

TL;DR

This paper presents a method to extract the spectrum of heavy particles from low-energy effective field theory coefficients using new analytic dispersion relations.

Contribution

It introduces a novel class of nonlinear dispersion relations that enable direct extraction of heavy particle spectra from effective field theory data.

Findings

Exact spectrum extraction for finite resonances

Approximate extraction when resonances are infinite

Applicable to broad class of theories and kinematics

Abstract

We show that the tree-level spectrum of heavy particles can be directly extracted from the Wilson coefficients of the corresponding effective field theory at low energies. This procedure is exact when the number of resonances is finite, and otherwise approximate. Our results are derived from a new class of analytic dispersion relations that depend nonlinearly on the scattering amplitude and apply to an exceedingly broad class of theories and kinematics.