Spectral and Transport Properties from Lattice QCD

Abstract

AbstractIn these lecture notes we will discuss recent progress in extracting spectral and transport properties from lattice QCD. We will focus on results of probes of the thermal QCD medium as well as transport coefficients that are important ingredients for hydrodynamic and transport models that describe the evolution of the produced medium. These include electromagnetic probes, like the rates of emitted photons and dileptons, quarkonium spectral functions, and transport coefficients, like the electrical conductivity or heavy flavor diffusion coefficients, of the quark gluon plasma (QGP). All these real-time quantities are encoded in the vector meson spectral functions. A direct determination of the spectral functions is not possible in Euclidean lattice QCD calculations. Fortunately the spectral functions can be analytically continued from imaginary to real time, i.e., they are even equivalent in real and imaginary time. Therefore it is possible to relate the spectral function to the corresponding Euclidean correlation functions, although this requires a spectral reconstruction to obtain it from the corresponding correlation functions. In the following sections we will discuss the procedure to determine the required correlation functions and the extraction of the spectral functions from lattice QCD correlators. We will illustrate the concepts and methods to obtain spectral functions and related physical observables. We will focus here on results obtained from continuum extrapolated correlation functions, which requires large and fine lattices, which so far was only possible to obtain in the so-called quenched approximation, where the effects of dynamical degrees of freedom in the medium are neglected. We will only give a brief introduction to lattice QCD and refer to the textbooks [1,2,3,4] and lecture notes [5] for more detailed introductions to lattice field theory. For the topics addressed in this lecture note we also like to refer to the overview articles on QCD thermodynamics and the QCD phase transition [5,6,7] and quarkonium in extreme conditions [8].