Hard-Thermal-Loop Resummation of the Free Energy of a Hot Gluon Plasma

We calculate the free energy of a hot gluon plasma to leading order in hard-thermal-loop perturbation theory. Effects associated with screening, gluon quasiparticles, and Landau damping are resummed to all orders. The ultraviolet divergences generated by the hard-thermal-loop propagator corrections can be canceled by a counterterm which depends on the thermal gluon mass. The deviation of the hard-thermal-loop free energy from lattice QCD results for $T>\mathrm{}{2T}_c$ has the correct sign and roughly the correct magnitude to be accounted for by next-to-leading order corrections.