NT/RIKEN

The shear and bulk viscosities of QCD are understood to have non-trivial temperature dependence. The quark-gluon plasma created at RHIC and the LHC provides a unique probe of this temperature dependence for temperatures ranging from ∼150 ~MeV to ∼400−600 MeV. Values of viscosities commonly quoted for the quark-gluon plasma, e.g. η/s∼0.1−0.2 for the shear viscosity to entropy density ratio, are understood to represent ``effective viscosities'', which combine the actual temperature-dependence of the transport coefficient with the complex temperature profile of the quark-gluon plasma. Using 0+1D Bjorken hydrodynamics as starting point, we provide a precise definition of effective viscosity for first-order (Navier-Stokes) hydrodynamics. We examine the role of the equation of state by comparing a QCD fluid with a conformal one. We use this definition of effective viscosity to obtain families of bulk viscosities ζ/s(T) that have different temperature dependence but nevertheless produce matching temperature evolutions in 0+1D hydrodynamics. We further extend the definition of effective viscosity to second-order (Israel-Stewart) Bjorken hydrodynamics. We express the second-order effective viscosity in terms of the initial bulk pressure of the system and its first-order effective viscosity, and quantify the approximate degeneracy of these latter two quantities in Bjorken hydrodynamics. We discuss extensions of this work beyond 0+1D, and review implications for phenomenological studies of heavy ion collisions.