Stochastic reconstructions of spectral functions: Application to lattice QCD

TL;DR

This paper compares two stochastic methods, SOM and SAI, for extracting spectral functions from lattice QCD data, demonstrating their consistency with the maximum entropy method and applying them to charmonia correlators at finite temperature.

Contribution

It provides a detailed comparison of stochastic optimization and analytical inference methods with MEM for spectral function reconstruction in lattice QCD, including applications to charmonia.

Findings

SAI and SOM yield results consistent with MEM at different temperatures.

Both stochastic methods effectively reconstruct spectral functions from model and lattice data.

The methods do not require prior information, making them versatile tools.

Abstract

We present a detailed study of the applications of two stochastic approaches, stochastic optimization method (SOM) and stochastic analytical inference (SAI), to extract spectral functions from Euclidean correlation functions. SOM has the advantage that it does not require prior information. On the other hand, SAI is a more generalized method based on Bayesian inference. Under mean field approximation SAI reduces to the often-used maximum entropy method (MEM), and for a specific choice of the prior SAI becomes equivalent to SOM. To test the applicability of these two stochastic methods to lattice QCD, firstly, we apply these methods to various reasonably chosen model correlation functions, and present detailed comparisons of the reconstructed spectral functions obtained from SOM, SAI and MEM. Next, we present similar studies for charmonia correlation functions obtained from lattice QCD computations using clover-improved Wilson fermions on large, fine, isotropic lattices at $0.75$ and $1.5T_c$, $T_c$ being the deconfinement transition temperature of a pure gluon plasma. We find that SAI and SOM give consistent results to MEM at these two temperatures.