  We extend a previous investigation of the QCD phase diagram with heavy quarks
in the context of background field methods by including the two-loop
corrections to the background field effective potential. The nonperturbative
dynamics in the pure-gauge sector is modeled by a phenomenological gluon mass
term in the Landau-DeWitt gauge-fixed action, which results in an improved
perturbative expansion. We investigate the phase diagram at nonzero temperature
and (real or imaginary) chemical potential. Two-loop corrections yield an
improved agreement with lattice data as compared to the leading-order results.
We also compare with the results of nonperturbative approaches. We further
study the equation of state as well as the thermodynamic stability of the
system at two-loop order. Finally, we show, using simple thermodynamic
arguments, that the behavior of the Polyakov loops as functions of the chemical
potential complies with their interpretation in terms of quark and anti-quark
free energies.
