Hadronic Structure, Conformal Maps, and Analytic Continuation

TL;DR

This paper introduces a new method for analytically continuing Green functions using conformal maps, providing rigorous uncertainty bounds and interpreting the results as smeared spectral functions, applicable to lattice QCD data.

Contribution

The paper develops a novel conformal map-based approach with systematic uncertainty bounds for analytic continuation of Green functions from Euclidean to real-time domains.

Findings

Provides a rigorous framework for uncertainty quantification.

Enables interpretation of Green functions as smeared spectral functions.

Applicable to lattice QCD computations.

Abstract

We present a method for analytic continuation of retarded Green functions, including Euclidean Green functions computed using lattice QCD. The method is based on conformal maps and construction of an interpolation function which is analytic in the upper half plane. A novel aspect of our method is rigorous bounding of systematic uncertainties, which are handled by constructing the full space of interpolating functions (at each point in the upper half-plane) consistent with the given Euclidean data and the constraints of analyticity. The resulting Green function in the upper half-plane has an appealing interpretation as a smeared spectral function.