# On the extraction of spectral densities from lattice correlators

## TL;DR

This paper introduces a novel, general method for extracting smeared spectral densities from lattice correlators, effectively handling uncertainties and enabling consistent infinite volume limit analysis, with potential applications beyond lattice QCD.

## Contribution

A new, flexible method for spectral density extraction from lattice correlators that incorporates smearing functions and uncertainty estimates, applicable across various inverse problems.

## Key findings

- Provides a way to choose smearing functions at the start.
- Enables consistent analysis across different volumes.
- Offers reliable uncertainty estimates for spectral densities.

## Abstract

Hadronic spectral densities are important quantities whose non-perturbative knowledge allows for calculating phenomenologically relevant observables, such as inclusive hadronic cross-sections and non-leptonic decay-rates. The extraction of spectral densities from lattice correlators is a notoriously difficult problem because lattice simulations are performed in Euclidean time and lattice data are unavoidably affected by statistical and systematic uncertainties. In this paper we present a new method for extracting hadronic spectral densities from lattice correlators. The method allows for choosing a smearing function at the beginning of the procedure and it provides results for the spectral densities smeared with this function together with reliable estimates of the associated uncertainties. The same smearing function can be used in the analysis of correlators obtained on different volumes, such that the infinite volume limit can be studied in a consistent way. While the method is described by using the language of lattice simulations, in reality it is completely general and can profitably be used to cope with inverse problems arising in different fields of research.