Calculation of the gluon damping rate in hot QCD

We present a complete calculation of the gluon damping rate at zero momentum to leading order in the QCD coupling constant $g$. All terms of leading order in $g$ are included by the resummation of an infinite subset of higher-loop diagrams. At zero momentum, the damping rates for transverse gluons and plasmons are equal: the result is $\gamma \simeq +0.264013\mathrm{}{g}^{2}T$, where $T$ is the temperature. The sign is positive, which implies that the quark-gluon plasma is perturbatively stable.