One-loop QCD corrections to the thermal Wilson line model

We calculate the time independent four-point function in high temperature (T) QCD and obtain the leading momentum dependent terms. Furthermore, we relate these derivative interactions to derivative terms in a recently proposed finite T effective action based on the SU(3) Wilson line and its trace, the Polyakov loop. By this procedure we thus obtain a perturbative matching at finite T between QCD and the effective model. In particular, we calculate the leading perturbative QCD correction to the kinetic term for the Polyakov loop.