Bulk viscosity in optimized perturbation theory

Full text. Many efforts have been made to understand the quark matter formed at high temperatures. It was expected that deconfined quark matter formed at high temperature should behave like a gas of weakly interacting quark- gluon plasma (wQGP). It is now believed that the system created at RHIC is a strongly coupled quark-gluon plasma (sQGP) and behaves like a nearly 'perfect' fluid. In order to understand the fluid properties of the formed plasma, the crucial quantities to be computed are the transport coefficients. One such transport coefficient of interest is the shear viscosity over entropy density η/s, which is required to be very small and close to the the lower bound η/s = 1=4π to fit the elliptic flow at RHIC from hydrodynamic simulation. In fluid dynamics, there is another important transport coefficient, the bulk viscosity ζ, which has often been neglected in hydrodynamic simulation of nuclear collisions. The zero bulk viscosity is for a conformal equation of state and also a reasonable approximation for the weakly interacting gas of quarks and gluons. For example, the perturbative QCD calculation gives very small values for ζ/s. However, recent lattice QCD results show that the bulk viscosity over entropy density ratio ζ/s rises dramatically up to the order of 1.0 near the critical temperature Tc. An alternative nonperturbative approach to study QCD phase transition is by using effective models. There is still no satisfied dynamic model that can describe deconfinement phase transition successfully. We thus focus on effective models which can describe chiral symmetry restoration. It has been argued that the chiral phase transition at finite chemical potential near critical point belongs to the Z(2) universality class. This motivates us to study the thermodynamic and transport properties of scalar model with symmetry Z(2) near phase transition in this paper. We will study the thermodynamic and transport properties in Optimized Perturbation Theory (OPT) formalism. At finite temperature, the naive perturbative expansion in powers of the coupling constant breaks down, and OPT formalism provides a convenient resummation method as we show recently. (author)