  It is shown that to leading order the collisional energy loss of an energetic
parton in the hot quark gluon plasma reads $dE/dx \sim \alpha(m_D^2)T^2$, where
the scale of the coupling is determined by the (parametrically soft) Debye
screening mass. Compared to previous expressions derived by Bjorken and other
authors, $dE^B/dx \sim \alpha^2 T^2 \ln(ET/m_D^2)$, the rectified result takes
into account the running of the coupling, as dictated by quantum corrections
beyond tree level. As one significant consequence, due to asymptotic freedom,
the QCD collisional energy loss becomes independent of the jet energy in the
limit $E \gg T$. It is advocated that this resummation improved perturbative
result might be useful to (re-)estimate the collisional energy loss for
temperatures relevant in heavy ion phenomenology.
