Pressure Isotropization in Heavy Ion Collisions from Color Glass Condensate

It is well known that the quark-gluon plasma (QGP) produced in heavy ion collisions can be successfully described by hydrodynamics; successful hydrodynamics requires rapid thermalization with the thermalization time τ0 less than 1 fm/c [1]. Studying the dynamical processes before the formation of the QGP can provide initial conditions for the hydrodynamic simulations. During the hydrodynamic evolution, the system is assumed to be close to local thermal equilibrium so that the use of thermodynamic quantities and relations are justified. On the other hand, ideal hydrodynamics implies that the system is isotropic in the local rest frame while viscous hydrodynamics could accomodate a small amount of anisotropy. Considering the initial conditions, a natural question to ask is whether the system becomes isotropic at or before the thermalization time τ0. The question is significant in the sense that isotropization is closely related to thermalization. Study of the isotropization problem can be beneficial to the understanding of the early thermalization puzzle. Furthermore, unraveling the isotropization process can determine whether we need isotropic or anisotropic initial conditions for the subsequent hydrodynamic evolutions. The problem has already been explored by several authors. Heller, Janik and Witaszczyk [2] approached the problem by studying the strongly coupled plasma in the N = 4 supersymmetric gauge theory under the AdS/CFT correspondence. They found sizable anisotropy at the transition to hydrodynamics ∆PL ≡ 1−PL/(ε/3) ∼ 0.7, where PL and PT are the longitudinal and transverse pressure and ε is the energy density. Epelbaum and Gelis [3] numerically solved the classical Yang-Mills equations incorporating initial quantum fluctuations in the Color Glass Condensate (CGC) framework. They found, when the strong coupling constant is taken gs = 0.5, large pressure anisotropy PL/PT ≈ 0.01 around the time 1/Qs (Qs is the gluon saturation scale) for classical initial conditions and PL/PT ≈ 0.6 for the situation including initial quantum fluctuations. Finally, Strickland [4] argued for the pressure anisotropy in the QGP from the viscous hydrodynamics itself and proposed an anisotropic hydrodynamics.