  Employing a non-perturbative gauge invariant definition of the Debye
screening mass m_D in the effective field theory approach to finite T QCD, we
use 3d lattice simulations to determine the leading O(g^2) and to estimate the
next-to-leading O(g^3) corrections to m_D in the high temperature region. The
O(g^2) correction is large and modifies qualitatively the standard
power-counting hierarchy picture of correlation lengths in high temperature
QCD.
