Towards a Theory of Binary Bound States in the Quark-Gluon Plasma

Although at temperatures $T\gg \Lambda_{QCD}$ the quark-gluon plasma (QGP) is a gas of weakly interacting quasiparticles (modulo long-range magnetism), it is strongly interacting in the regime $T=(1-3) T_c$. As both heavy ion experiments and lattice simulations are now showing, in this region the QGP displays rather strong interactions between the constituents. In this paper we investigate the relationship between four (previously disconnected) lattice results: {\bf i.} spectral densities from MEM analysis of correlators; {\bf ii.} static quark free energies $F(R)$; {\bf iii.} quasiparticle masses; {\bf iv.} bulk thermodynamics $p(T)$. We show a high degree of consistency among them not known before. The potentials $V(R)$ derived from $F(R)$ lead to large number of binary bound states, mostly colored, in $gq, qq, gg$, on top of the usual $\bar q q$ mesons. Using the Klein-Gordon equation and ({\bf ii-iii}) we evaluate their binding energies and locate the zero binding endpoints on the phase diagram, which happen to agree with ({\bf i}). We then estimate the contribution of all states to the bulk thermodynamics in agreement with ({\bf iv}). We also address a number of theoreticall issues related with to the role of the quark/gluon spin in binding at large $\alpha_s$, although we do not yet include those in our estimates. Also the issue of the transport properties (viscosity, color conductivity) in this novel description of the QGP will be addressed elsewhere.