The non-perturbative QCD Debye mass from a Wilson line operator

According to a proposal by Arnold and Yaffe, the non-perturbative g^2T-contribution to the Debye mass in the deconfined QCD plasma phase can be determined from a single Wilson line operator in the three-dimensional pure SU(3) gauge theory. We extend a previous SU(2) measurement of this quantity to the physical SU(3) case. We find a numerical coefficient which is more accurate and smaller than that obtained previously with another method, but still very large compared with the naive expectation: the correction is larger than the leading term up to T ~ 10^7 T_c, corresponding to g^2 ~ 0.4. At moderate temperatures T ~ 2 T_c, a consistent picture emerges where the Debye mass is m_D ~ 6T, the lightest gauge invariant screening mass in the system is ~ 3T, and the purely magnetic operators couple dominantly to a scale ~ 6T. Electric (~ gT) and magnetic (~ g^2T) scales are therefore strongly overlapping close to the phase transition, and the colour-electric fields play an essential role in the dynamics.