Spectral densities from Euclidean-time lattice correlation functions

TL;DR

This paper reviews a new strategy for extracting spectral densities from Euclidean-time lattice correlation functions in quantum field theories, addressing the ill-posed inverse Laplace transform problem in Lattice QCD.

Contribution

It introduces a novel method for non-perturbative spectral density extraction applicable to both continuum and lattice cases, including smeared densities.

Findings

Effective inversion strategy for spectral densities

Applicable to continuum and lattice QCD

Handles smeared spectral densities

Abstract

In quantum field theories, spectral densities are directly related to relevant physical observables. In Lattice QCD, their non-perturbative extraction from first principles requires the Inverse Laplace transform of Euclidean-time correlation functions, a notorious ill-posed problem. Here we review our recent proposal [1,2] for a new strategy to perform this inversion both in the continuum and on the lattice, also suitable for smeared spectral densities, both in the continuum and in the discrete cases.