Finite-size effects and finite-size scaling in time evolution during a colorless confining phase transition

Abstract

The time evolution of the expanding colorless partonic matter, created in ultra-relativistic heavy ion collisions and undergoing the confining phase transition, is discussed in the context of our colorless QCD-MIT bag model with the boost invariant Bjorken expansion and using the -method. The direct extension of this method to the non-colorless case is clearly formulated. The hydrodynamic equation in the case of a longitudinal expansion scenario of a non-ideal relativistic medium in finite volume is solved using certain initial conditions . The evolution of the temperature T(τ,V) as a function of the proper time and of the volume is then obtained. Different times characterising the whole time evolution, like the time at which the confining phase transition begins τ P (V), the hadronic time at which the hadronization is completed, the lifetime of the Colorless Partonic Plasma and the lifetime of the confining phase transition are carefully extracted and their finite-size scaling properties are studied in detail and compared with the derived laws. The effects of the initial conditions (T i , τ i ) on different times and lifetimes are investigated in detail. We find that the time evolution of our system is really affected by the colorlessness requirement.