Shear viscosity of the Quark–Gluon Plasma from a virial expansion
Institute for Theoretical Physics, University of Gießen, Gießen, Germany
Revised: 19 July 2010
Published online: 16 October 2010
We calculate the shear viscosity η in the quark–gluon plasma (QGP) phase within a virial expansion approach with particular interest in the ratio of η to the entropy density s, i.e. η/s. The virial expansion approach allows us to include the interactions between the partons in the deconfined phase and to evaluate the corrections to a single-particle partition function. In the latter approach we start with an effective interaction with parameters fixed to reproduce thermodynamical quantities of QCD such as energy and/or entropy density. We also directly extract the effective coupling α V for the determination of η. Our numerical results give a ratio η/s≈0.097 at the critical temperature T c, which is very close to the theoretical bound of 1/(4π). Furthermore, for temperatures T≤1.8T c the ratio η/s is in the range of the present experimental estimates 0.1–0.3 at RHIC. When combining our results for η/s in the deconfined phase with those from chiral perturbation theory or the resonance-gas model in the confined phase we observe a pronounced minimum of η/s close to the critical temperature T c.
© Springer-Verlag / Società Italiana di Fisica, 2010