The shear viscosity of parton matter under anisotropic scatterings

Abstract

The shear viscosity $$\eta $$ η of a quark–gluon plasma in equilibrium can be calculated analytically using multiple methods or numerically using the Green–Kubo relation. It has been realized, which we confirm here, that the Chapman–Enskog method agrees well with the Green–Kubo result for both isotropic and anisotropic two-body scatterings. We then apply the Chapman–Enskog method to study the shear viscosity of the parton matter from a multi-phase transport model. In particular, we study the parton matter in the center cell of central and midcentral Au + Au collisions at 200A GeV and Pb + Pb collisions at 2760A GeV, which is assumed to be a plasma in thermal equilibrium but partial chemical equilibrium. As a result of using a constant Debye mass or cross section $$\sigma $$ σ for parton scatterings, the $$\eta /s$$ η / s ratio increases with time (as the effective temperature decreases), contrary to the trend preferred by Bayesian analysis of the experimental data or pQCD results that use temperature-dependent Debye masses. At $$\sigma =3$$ σ = 3 mb that enables the transport model to approximately reproduce the elliptic flow data of the bulk matter, the average $$\eta /s$$ η / s of the parton matter in partial equilibrium is found to be very small, between one to two times $$1/(4\pi )$$ 1 / ( 4 π ) .

Anisotropic particle in viscous shear flow : navier slip, reciprocal symmetry, and jeffery orbit

“…where σ p is the partonic scattering cross section, g(w) is the thermal average of h(a) = 4a(1 + a)[(1 + 2a) ln(1 + 1 a ) − 2] and can be approximated as [15,24]…”

“…The AMPT model includes the transport process that simulates parton interactions and has a natural shear viscosity that is analytically or numerically calculable, dependent on the scattering cross section, in kinetic theory such as Israel-Stewart (IS) or Chapman-Enskog (CE) methods [15]. For a fixed parton scattering cross section, the temperature dependence of the shear viscosity of parton matter estimated using the IS method in the AMPT model is opposite to that suggested by perturbative QCD and Bayesian analysis of the experimental data, which shows that the ratio of shear viscosity to entropy density increases as the temperature decreases [16,17].…”

“…The relationship of shear viscosity with scattering cross section and temperature in IS method can be used to simulate the evolution process of partons with parameterized * yaozhang@jxust.edu.cn shear viscosity in the AMPT model [18,19]. While the IS method is suited for isotropic scattering, partons in the AMPT model undergo forward-angle scattering, necessitating the use of the CE method that is better adapted for anisotropic scattering to estimate the shear viscosity [15,20,21]. With the shear viscous transport dynamics simulation corrected by the CE method, we simulate Au+Au collisions at √ s N N = 200GeV in the AMPT model with const η/s which is less affected by temperature dependence at RHIC energy.…”