Extraction of spectral densities from lattice correlators: decoupling signal from noise

TL;DR

This paper introduces an alternative method for extracting smeared spectral densities from Euclidean correlators that avoids Backus-Gilbert regularization by decomposing the solution into a sum of terms, optimizing the signal-to-noise ratio.

Contribution

It proposes a novel approach based on singular value decomposition to improve spectral density extraction by better managing noise and systematics.

Findings

The method effectively separates signal from noise in spectral density extraction.

Optimal truncation of the solution sum enhances the accuracy of the spectral density.

The approach can complement existing regularization techniques like Backus-Gilbert.

Abstract

We expand the treatment of the problem of the extraction of smeared spectral densities from Euclidean correlators introduced in [Phys. Rev. D 99, 094508], providing an alternative which does not rely on the Backus-Gilbert regularization. This is possible due to the observation that the solution can be decomposed into a sum of terms, in the spirit of the singular value decomposition, where those with the largest contribution to the statistical noise happen to contribute the least to the central value of the smeared spectral density. The analysis of the systematics of the inverse problem is then shifted to finding the optimal truncation of such summation, so that the signal is saturated before the noise explodes. We scrutinise the performance and systematics of this approach either as a standalone procedure, or to complement the stability analysis required to extrapolate the unbiased result in the Backus-Gilbert regulated version of the solution.