A stochastic approach to the reconstruction of spectral functions in lattice QCD

TL;DR

This paper introduces a stochastic optimization method for reconstructing spectral functions from lattice QCD data, effectively handling sharp features and continuum spectra, and providing comparable results to existing methods.

Contribution

The paper presents a novel stochastic approach for spectral function reconstruction that improves upon traditional methods like Maximum Entropy in lattice QCD analysis.

Findings

Successfully reconstructs mock spectral functions with sharp peaks and continua

Analyzes charmonium correlators and finds consistent dissociation temperatures

Demonstrates the method's effectiveness comparable to established techniques

Abstract

We present a Stochastic Optimization Method (SOM) for the reconstruction of the spectral functions (SPFs) from Euclidean correlation functions. In this approach the SPF is parameterized as a sum of randomly distributed boxes. By varying the width, location and height of the boxes stochastically an optimal SPF can be obtained. Using this approach we reproduce mock SPFs fairly well, which contain sharp resonance peaks, transport peaks and continuum spectra. We also analyzed the charmonium correlators obtained from $N_{\tau}$=96, 48, 32 lattices using SOM and found similar conclusion on the dissociation temperatures of charmonium ground states as that obtained using the Maximum Entropy Method.