  Thermal field theory is indispensable for describing hot and dense systems.
Yet perturbative calculations are often stymied by a host of energy scales, and
tend to converge slowly. This means that precise results require the apt use of
effective field theories. In this paper we refine the effective description of
slowly varying gauge field known as hard thermal loops. We match this effective
theory to the full theory to two-loops. Our results apply for any
renormalizable model and fermion chemical potential. We also discuss how to
consistently define asymptotic masses at higher orders; and how to treat
spectral functions close to the lightcone. In particular, we demonstrate that
the gluon mass is well-defined to next-to-leading order.
