Maximum Entropy Analysis of the Spectral Functions in Lattice QCD

TL;DR

This paper reviews the use of the Maximum Entropy Method for extracting spectral functions from lattice QCD data, highlighting its advantages and demonstrating its effectiveness with mock and real data.

Contribution

It introduces and explains the application of MEM to lattice QCD spectral functions, emphasizing its non-parametric nature and quantitative analysis capabilities.

Findings

MEM accurately reproduces low-energy resonances

It reveals the high-energy continuum in hadronic correlators

Demonstrates MEM's effectiveness with mock and lattice data

Abstract

First principle calculation of the QCD spectral functions (SPFs) based on the lattice QCD simulations is reviewed. Special emphasis is placed on the Bayesian inference theory and the Maximum Entropy Method (MEM), which is a useful tool to extract SPFs from the imaginary-time correlation functions numerically obtained by the Monte Carlo method. Three important aspects of MEM are (i) it does not require a priori assumptions or parametrizations of SPFs, (ii) for given data, a unique solution is obtained if it exists, and (iii) the statistical significance of the solution can be quantitatively analyzed. The ability of MEM is explicitly demonstrated by using mock data as well as lattice QCD data. When applied to lattice data, MEM correctly reproduces the low-energy resonances and shows the existence of high-energy continuum in hadronic correlation functions. This opens up various possibilities for studying hadronic properties in QCD beyond the conventional way of analyzing the lattice data. Future problems to be studied by MEM in lattice QCD are also summarized.