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Recently, a finite-temperature real-time static potential has been introducedvia a Schr\"odinger-type equation satisfied by a certain heavy quarkoniumGreen's function. Furthermore, it has been pointed out that it possesses animaginary part, which induces a finite width for the tip of the quarkonium peakin the thermal dilepton production rate. The imaginary part originates fromLandau-damping of low-frequency gauge fields, which are essentially classicaldue to their high occupation number. Here we show how the imaginary part can bemeasured with classical lattice gauge theory simulations, accountingnon-perturbatively for the infrared sector of finite-temperature field theory.We demonstrate that a non-vanishing imaginary part indeed existsnon-perturbatively; and that its value agrees semi-quantitatively with thatpredicted by Hard Loop resummed perturbation theory.

Thermal imaginary part of a real-time static potential from classical lattice gauge theory simulations