$T$-matrix Approach to Quark-Gluon Plasma.

A selfconsistent thermodynamic $T$-matrix approach is deployed to study the microscopic properties of the quark-gluon plasma (QGP), encompassing both light- and heavy-parton degrees of freedom in a unified framework. The starting point is a relativistic effective Hamiltonian with a universal color force. The input in-medium potential is quantitatively constrained by computing the heavy-quark (HQ) free energy from the static $T$-matrix and fitting it to pertinent lattice-QCD (lQCD) data. The corresponding $T$-matrix is then applied to compute the equation of state (EoS) of the QGP in a two-particle irreducible formalism including the full off-shell properties of the selfconsistent single-parton spectral functions and their two-body interaction. In particular, the skeleton diagram functional is fully resummed to account for emerging bound and scattering states as the critical temperature is approached from above. We find that the solution satisfying three sets of lQCD data (EoS, HQ free energy and quarkonium correlator ratios) is not unique. As limiting cases we discuss a weakly-coupled solution (WCS) which features color-potentials close to the free energy, relatively sharp quasiparticle spectral functions and weak hadronic resonances near $T_{\rm c}$, and a strongly-coupled solution (SCS) with a strong color potential (much larger than the free energy) resulting in broad non-quasiparticle parton spectral functions and strong hadronic resonance states which dominate the EoS when approaching $T_{\rm c}$.