Shear viscosity of pion gas

Shear viscosity η is one of transport coefficients in fluid dynamics, which characterizes how viscous the system is in the presence of flow gradient [1]. Since, in general, shear viscosity is inversely proportional to scattering cross-section, strongly interacting systems have smaller viscosity than weakly interacting ones. Recently a universal minimum bound for the ratio of η to entropy density s has been proposed by Kovtun, Son, and Starinets (KSS) [2]. The bound, η/s ≥ 1 4π , is conjectured to be satisfied for a large class of strongly interacting quantum field theories whose dual descriptions in string theory involve black holes in anti-de Sitter space [3, 4, 5, 6]. Note that η/s is more physical quantity than η itself because the ratio appears as a diffusion constant of fluid equations. In experiments, η/s close to the minimum bound were found in relativistic heavy ion collisions (RHIC) [7, 8, 9]. This discovery came as a surprise. Traditionally, quark gluon plasma (QGP), a phase of the quantum chromodynamics (QCD) above the deconfinement temperature Tc ∼ 170 MeV at zero baryon density [10], had been thought to be in weak interaction regime. Partly because lattice QCD simulations of the QGP equation of state above 2Tc are not inconsistent with that of an ideal gas of massless particles, e = 3p, where e is the the energy density and p is the pressure of the system [10]. However, recent analyses of the elliptic flow generated by non-central collisions in RHIC [8, 9] and lattice simulations of a gluon plasma [11] yielded η/s close to the the minimum bound at just above Tc. This suggests QGP is strongly interacting at this temperature. 1 Other implications for strong coupling can be seen in sharp peaks of mesonic correlators [12, 13, 14], and in discussions of the possible microscopic structure of such a state [16, 17, 18, 19, 20]. Given this situation, one naturally gets interested in how η/s behaves as temperature approaches Tc from below, supposing that η/s of QCD was