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

TL;DR

This work posits that the quark-gluon plasma near the deconfinement temperature is a strongly coupled Coulomb system populated by a large number of binary bound states across colored and colorless channels. By correlating lattice-derived static potentials, spectral densities, quasiparticle masses, and bulk thermodynamics, the authors build a self-consistent picture in which bound states significantly contribute to the QGP's thermodynamics; they show charmonium and light bound states can persist up to roughly $2-3\,T_c$, with color-bound states becoming important near $T_c$ and diminishing at higher temperatures. The analysis combines relativistic two-body bound-state formalisms, lattice potential extraction, and Beth-Uhlenbeck-type thermodynamics, emphasizing the roles of Casimir-scaled color forces, relativistic corrections, and instanton-induced interactions in shaping the spectrum and thermodynamics. These results suggest that a bound-state gas, rather than a pure quasiparticle gas, can account for the observed bulk properties of the QGP in the not-too-high-temperature regime, with implications for transport and chiral dynamics to be explored further.

Abstract

Although at temperatures $T\gg Λ_{QCD}$ 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 $α_s$, 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.

Figures (9)

• Figure 1: Schematic position of several zero binding lines on the QCD phase diagram, from SZ1.
• Figure 2: The pressure normalized to that of a gas of massless and noninteracting quasiparticles, or Stephan-Boltzmann value, versus the temperature $T/T_c$, from the lattice calculations by the Bielefeld group Karsch_pressure. Different curves are for different numbers (masses) of the dynamical quarks.
• Figure 3: Classical motion of two mutually attracting charges. If the field propagation is instantaneous, a partner of a particle P is at the "antipode" point A. However if particles move relativistically and the electromagnetic field travels at light speeds, the particle P sees a field from the earlier position B (drawn for counterclockwise rotation).
• Figure 4: Heavy quark free energies in the singlet channel for 2-flavors of dynamical quarks at a quark mass of $m/T=0.40$ on $16^3\times 4$ lattices renormalized to the zero-$T$ potential obtained from Kaczmarek:2003ph.
• Figure 5: The color singlet screening function, from Kaczmarek:2003ph.