Real Time Quarkonium Transport Coefficients in Open Quantum Systems from Euclidean QCD

TL;DR

This paper investigates how to extract quarkonium transport coefficients from Euclidean QCD correlators using lattice methods, addressing challenges like spectral function reconstruction and renormalon uncertainties.

Contribution

It provides a framework for calculating quarkonium transport coefficients from Euclidean correlators and discusses differences between adjoint and fundamental coefficients at finite temperature.

Findings

Euclidean correlator extraction of transport coefficients is feasible with lattice QCD.

The difference between $\gamma_{ m adj}$ and $\gamma_{ m fund}$ appears at $\mathcal{O}(g^4)$.

Strategies to reduce infrared renormalon uncertainties in lattice calculations are proposed.

Abstract

Recent open quantum system studies showed that quarkonium time evolution inside the quark-gluon plasma is determined by transport coefficients that are defined in terms of a gauge invariant correlator of two chromoelectric field operators connected by an adjoint Wilson line. We study the Euclidean version of the correlator for quarkonium evolution and discuss the extraction of the transport coefficients from this Euclidean correlator, highlighting its difference from other problems that also require reconstructing a spectral function, such as the calculation of the heavy quark diffusion coefficient. Along the way, we explain why the transport coefficient $\gamma_{\rm adj}$ differs from $\gamma_{\rm fund}$ at finite temperature at $\mathcal{O}(g^4)$, in spite of the fact that their corresponding spectral functions differ only by a temperature-independent term at the same order. We then discuss how to evaluate the Euclidean correlator via lattice QCD methods, with a focus on reducing the uncertainty caused by infrared renormalons in determining the renormalization factor nonperturbatively.