Nonperturbative Debye Mass in Finite Temperature QCD

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