Critical Behavior Of The Shear Viscosity In Hot ?~4 Theory

In the relativistic heavy-ion collision,the generated hot and dense matter quark-gluon plasma QGP evolve from nonequilibrium to equilibrium and must undergo a series of transport process,accompanied with hadronization.Viscous phenomenon exists commonly in the transport process.The relevant characteristic parameter is the shear viscosity,whose critical behavior has important research value.For example,figuring out the fluid properties of quark-gluon plasmon,locating the critical point,etc.The ratio of the shear viscosity to the entropy density is dimensionless and universal,which is widly studied in the current literature.Within the frame of the finite temperature field theory,in terms of the hot and dense matter plasma which is spontaneous symmetry breaking in the hot ?4 theory,we study the critical behaviour of the viscosity of the plasma.We respectively check the dependence of the shear viscosity and the entropy density on temperature and coupling constant.Referring to the research of the damping rate of the spontaneous symametry breaking plasma within the hot ?4 theory in the literature[6],We obtain the Wilson renormalization group equation of the mass and the coupling constant of the plasma.By means of the numerical analysis of the equation,we find the critical behaviour of the running coupling constant of the plasma.The numerical results show,if we ignore the running of the coupling constant with temperature,the ratio ?/s would be a constant as temperature approach the critical point.If we take the running of the coupling constant given by the Wilson renormalization equation around the critical area into account,the ratio ?/s will increase constantly when the plasma cool down to the critical point.This means,in the hot scalar field,the viscous force between layers of the fluid is stronger and stronger when phase transition the spontaneous symmetry breaking restoration to the spontaneous symmetry breaking,namely the critical viscosity of the plasma is higher.The current research on high energy heavy-ion collision,there are some views that the energy loss of the jet may anomaly enhance when QGP cool down to the critical point.The conclusion in our work about the critical enhancement of the shear viscosity of the plasma,may be the reference to the research on jet quenching.