Abstract
The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ~12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Highlights
If a system in thermodynamic equilibrium is displaced slightly by means of some external perturbation, it tends to relax back to equilibrium
Heavy quarks are naturally displaced from kinetic equilibrium, given that they are generated in an initial hard process which has no knowledge of the thermal state and the flow that it develops during ∼1 fm/c
The purpose of this technical contribution has been to report on the result of a 1-loop computation in lattice perturbation theory for the renormalization factor defined in eq (5.4)
Summary
If a system in thermodynamic equilibrium is displaced slightly by means of some external perturbation, it tends to relax back to equilibrium. Heavy quarks are naturally displaced from kinetic equilibrium, given that they are generated in an initial hard process which has no knowledge of the thermal state and the flow that it develops during ∼1 fm/c It is empirically observed, that the process of kinetic equilibration takes place during the fireball expansion: heavy quark jets get quenched, and eventually heavy quarks participate in hydrodynamic flow almost as efficiently as light quarks do One is taking the continuum limit: for a systematic extrapolation the electric field correlator requires a finite renormalization factor, which should be determined non-perturbatively. We compute the renormalization factor for the electric field correlator at 1-loop order in lattice perturbation theory [21,22], and briefly comment on the possibilities for non-perturbative renormalization With such ingredients and improved statistical precision, the current order-of-magnitude estimate [17] can hopefully be promoted towards a quantitative level. We offer an outlook and comments on non-perturbative renormalization in sec. 6
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