Spectral functions at small energies and the electrical conductivity in hot, quenched lattice QCD

TL;DR

This paper improves the reconstruction of spectral functions in lattice QCD at finite temperature, revealing a small electrical conductivity above the deconfinement transition by addressing instability issues in existing methods.

Contribution

It introduces a modified algorithm for spectral function reconstruction that overcomes Bryan's method instability at small energies in lattice QCD simulations.

Findings

The modified method provides stable spectral function reconstructions at small energies.

Results suggest a small electrical conductivity in the quark-gluon plasma.

The approach enhances the reliability of spectral analyses in finite-temperature lattice QCD.

Abstract

In lattice QCD, the Maximum Entropy Method can be used to reconstruct spectral functions from euclidean correlators obtained in numerical simulations. We show that at finite temperature the most commonly used algorithm, employing Bryan's method, is inherently unstable at small energies and give a modification that avoids this. We demonstrate this approach using the vector current-current correlator obtained in quenched QCD at finite temperature. Our first results indicate a small electrical conductivity above the deconfinement transition.