Perturbative versus Lattice QCD Energy Density Correlators at High Temperatures

Correlators of magnetic and electric field energy density are investigated for SU($N_c$) gauge theory at high temperatures $T$. At separations $z\leq 2/T$ the correlators are shown to be dominated by a power--law behavior even for finite gluon screening masses. This continuum behavior is well approximated on current $4\times 16^3$--lattices in the perturbative limit and leads to a considerable overestimate of screening masses deduced from fitting the lattice correlators with conventional exponential forms. The use of extended sources and sinks to enhance the signal improves the situation for screening masses $m\gg T$ but leads to a largely uncontrolled error for masses less than $T$. In fact, we show that recent lattice QCD data of Grossmann et al., from which a magnetic screening mass $m_M \approx 2.9 \, T$ was deduced, may even be consistent with a vanishing actual magnetic screening mass.