Beyond thresholds: reconstructing UV physics from IR expansions

TL;DR

This paper demonstrates how to extract ultraviolet physics information from low-energy expansions in quantum field theories by using inverse Laplace transforms and coarse-graining, enabling insights into the sign of the beta function and dynamical scales.

Contribution

It introduces a method to recover UV behavior from IR data, extending the utility of low-energy expansions beyond traditional cutoff limitations.

Findings

Determined the sign of the beta function from IR data.

Reconstructed the dynamical scale from low-energy observables.

Applied the method to QED and QCD-like theories.

Abstract

We show that ultraviolet information can be extracted from low-energy expansion coefficients, assuming analyticity and the absence of massless singularities. By reorganizing the low-energy expansion through an inverse Laplace transform and a controlled coarse-graining procedure, we make ultraviolet behavior accessible beyond the cutoff of the effective field theory. In particular, we determine the sign of the beta function and the associated dynamical scale directly from the low-energy expansion of a physical observable below the mass thresholds in QED and QCD-like theories.