Viscosity of the QGP from a virial expansion
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ELEMENTARY PARTICLES AND FIELDS Theory
Viscosity of the QGP from a Virial Expansion* S. Mattiello** Institute for Theoretical Physics, University of Gießen, Germany Received March 31, 2011
Abstract—In this work we calculate the shear viscosity η in the quark–gluon plasma within a virial expansion approach with particular interest in the ratio of η to the entropy density s, i.e. η/s. We derive a realistic equation of state using a virial expansion approach which allows us to include the interactions between the partons in the deconfined phase. From the interaction we directly extract the effective coupling αV for the determination of η. Our results for η/s show a minimum near to Tc very close with the lowest bound and, furthermore, in line with the experimental point from RHIC as well as with the lattice calculations. DOI: 10.1134/S1063778812060257
1. INTRODUCTION The experimental findings of the heavy-ion collisions at the Relativistic Ion Collider (RHIC) led to the announcement about the discovery of the nearly perfect fluidity of the strongly-coupled quark–gluon plasma (sQGP) [1, 2]. Ideal hydrodynamics seems to offer a good description for the experimental data for moderate momenta, in particular of the strong elliptic flow v2 . Nevertheless, ideal hydrodynamics gradually breaks down at larger impact parameter, at lower collision energy and away from midrapidity due to strong viscous effects. The key role of the viscous correction has been also addressed by the very recent v2 data for PbPb collision at the LHC [3]. Therefore a dynamic calculation of the shear viscosity η within a model describing the strong coupling properties of the QGP is mandatory. Recently, we have developed a generalization of the classical virial expansion approach to calculate the QCD partition function in the partonic phase with an interaction inspired by lattice calculations [4]. We have obtained an Equation of State (EoS) for the QGP that compares well with three-flavor QCD lattice data [5] at nonzero temperature and vanishing quark chemical potential (μq = 0). Since in the virial expansion approach all thermodynamic quantities are based on an explicit parton interaction in form of a potential, this approach is also the ideal starting point for a consistent description of dynamical properties of the sQGP like the shear viscosity η within kinetic theory. ∗ **
The text was submitted by the author in English. E-mail: [email protected]. uni-giessen.de
2. η/s AND VIRIAL EXPANSION In an ultrarelativistic quark–gluon plasma, where the temperature T is much larger than the constituent masses mi , the ratio of the shear viscosity η and the entropy density s can be estimated, following [6], as 4 T η ≈ . (1) s 5 sσt The relevant transport cross section is given by s) ≡ dσel sin2 θcm σt (ˆ
(2)
= σ0 · 4z(1 + z) [(2z + 1) ln(1 + 1/z) − 2], s) = 9πα2V (ˆ s)/2μ2scr . with the total cross section σ0 (ˆ Here, αV = αV (T ) and μscr are the effective temperature-dependent coupling constant and the screening s. For simplicity, we mass, respective
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