Bulk viscosity and spectral functions in QCD

TL;DR

This paper analyzes the spectral function of the stress tensor trace in QCD at weak coupling and near a phase transition, focusing on bulk viscosity behavior and challenges in lattice data analysis.

Contribution

It provides analytical insights into the spectral function and bulk viscosity in two key regimes of QCD, highlighting the difficulty of extracting spectral features from lattice data.

Findings

Spectral function exhibits a narrow peak at small frequency in both regimes.

Bulk viscosity behavior differs between weak coupling and near phase transition.

Challenges in accurately determining spectral functions from lattice data are discussed.

Abstract

We examine the behavior of the spectral function for the trace of the stress tensor in QCD in the two regimes where it is possible to make analytical progress; weak coupling, and close to a second order QCD phase transition. We determine the behavior of the bulk viscosity in each regime. We discuss the problem of analytic continuation of the (lattice) Euclidean correlation function to determine the spectral function. In each case the spectral function has a narrow peak at small frequency; its shape would be challenging to extract accurately from lattice data with error bars.