Phenomenological equations of state for the quark-gluon plasma

Two phenomenological models describing an SU(N) quark-gluon plasma are presented, The first is obtained from high temperature expansions of the free energy of a massive gluon, while the second is derived by demanding color neutrality over a certain length scale. Each model has a single free parameter, exhibits behavior similar to lattice simulations over the range T-d-5T(d), and has the correct blackbody behavior for large temperatures. The N=2 deconfinement transition is second order in both models, while N=3, 4, and 5 are first order. Both models appear to have a smooth targe-N limit. For Ngreater than or equal to4, it is shown that the trace of the Polyakov loop is insufficient to characterize the phase structure; the free energy is best described using the eigenvalues of the Polyakov loop. In both models, the confined phase is characterized by a mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop expectation value zero. In the deconfined phase, the rotation of the eigenvalues in the complex plane towards 1 is responsible for the approach to the blackbody limit over the range T-d-5T(d). The addition of massless quarks in SU(3) breaks Z(3) symmetry weakly and eliminates the deconfining phase transition. In contrast, a first-order phase transition persists with sufficiently heavy quarks.