Thermodynamic potential for quark-qluon plasma with finite quark masses and chemical potential

The thermodynamic potential for quarks in quantum chromodynamics (QCD) is a desired ingredi- ent for computations of the equation of state in supernovae, neutron stars, and heavy-ion collisions. We present a derivation of the finite-temperature, finite chemical potential thermodynamic poten- tial in QCD that includes finite quark masses in the Feynman diagram contributions for two-loop corrections to the quark interaction. These contributions are normally divergent and become even more difficult in the limit of finite quark masses at finite chemical potential. In this paper, however, we demonstrate that it is possible to compute the 2-loop corrections for both finite-mass and finite chemical potential in a limited range by incorporating a periodic renormalization in the evaluation of the two-loop diagrams and employing a Pade (or polynomial) interpolation between the finite mass and massless regimes as a function of chemical potential. We propose that this simple relativistic calculation is an improvement over previous semiclassical approaches to this correction.