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

Propagation of gauge fields in hot and dense plasmas at higher orders