We consider quarkonium in a hot quantum chromodynamics (QCD) plasma which, due to expansion and nonzero viscosity, exhibits a local anisotropy in momentum space. At short distances the heavy-quark potential is known at tree level from the hard-thermal loop resummed gluon propagator in anisotropic perturbative QCD. The potential at long distances is modeled as a QCD string which is screened at the same scale as the Coulomb field. At asymptotic separation the potential energy is nonzero and inversely proportional to the temperature. We obtain numerical solutions of the three-dimensional Schrödinger equation for this potential. We find that quarkonium binding is stronger at nonvanishing viscosity and expansion rate, and that the anisotropy leads to polarization of the $P$-wave states.

• Received 19 January 2009

DOI:https://doi.org/10.1103/PhysRevD.79.054019