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Recent open quantum system studies showed that quarkonium time evolutioninside the quark-gluon plasma is determined by transport coefficients that aredefined in terms of a gauge invariant correlator of two chromoelectric fieldoperators connected by an adjoint Wilson line. We study the Euclidean versionof the correlator for quarkonium evolution and discuss the extraction of thetransport coefficients from this Euclidean correlator, highlighting itsdifference from other problems that also require reconstructing a spectralfunction, 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 bya temperature-independent term at the same order. We then discuss how toevaluate the Euclidean correlator via lattice QCD methods, with a focus onreducing the uncertainty caused by infrared renormalons in determining therenormalization factor nonperturbatively.

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