# Transport coefficients from in medium quarkonium dynamics

## TL;DR

This paper estimates the transport coefficients $$ and $$ for in-medium quarkonium dynamics using lattice QCD data, providing the first non-perturbative determination of $$ and confirming previous results for $$.

## Contribution

It introduces a method to evaluate the transport coefficients $$ and $$ from lattice QCD data, including the first non-perturbative estimate of $$.

## Key findings

- The range for $$ aligns with earlier estimates.
- First non-perturbative estimate of $$ obtained.
- Results are relevant for understanding quarkonium in medium dynamics.

## Abstract

The in medium dynamics of heavy particles are governed by transport coefficients. The heavy quark momentum diffusion coefficient, $\kappa$, is an object of special interest in the literature, but one which has proven notoriously difficult to estimate, despite the fact that it has been computed by weak-coupling methods at next-to-leading order accuracy, and by lattice simulations of the pure SU(3) gauge theory. Another coefficient, $\gamma$, has been recently identified. It can be understood as the dispersive counterpart of $\kappa$. Little is known about $\gamma$. Both $\kappa$ and $\gamma$ are, however, of foremost importance in heavy quarkonium physics as they entirely determine the in and out of equilibrium dynamics of quarkonium in a medium, if the evolution of the density matrix is Markovian, and the motion, quantum Brownian; the medium could be a strongly or weakly coupled plasma. In this paper, using the relation between $\kappa$, $\gamma$ and the quarkonium in medium width and mass shift respectively, we evaluate the two coefficients from existing 2+1 flavor lattice QCD data. The resulting range for $\kappa$ is consistent with earlier determinations, the one for $\gamma$ is the first non-perturbative determination of this quantity.