Finite Size Scaling in Time Evolution During the Colorless-QCD 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 towards a Hadronic Gas, is discussed in the context of a unified model combining our Colorless QCD-MIT Bag Model with the boost invariant Bjorken expansion. The Bjorken Equation in the case of a longitudinal expansion scenario of a non-ideal relativistic medium in finite volume is solved using certain initial conditions $(\tau_i,T(\tau_i))$ and their effect is studied in detail. The evolution of the temperature as a function of the proper time $T(\tau,V)$ is then obtained at different volumes. Different times characterising different scales of the whole time evolution, like the time of the finite volume transition point $\tau_0(V)$, the hadronic time $\tau_H(V)$ at which the hadronization is completed, the lifetime of the Colorless Partonic Plasma $\Delta \tau_{CPP}(V)$ and the lifetime of the confining phase transition $\Delta \tau_{PT}(V)$ are calculated and their finite size scaling properties are studied in detail. New finite size scaling laws are derived. Also, the time evolution of some Thermal Response Functions as the order parameter $\mathcal{H}(\tau,V)$, energy density $\epsilon(\tau,V)$, pressure $\mathscr{P}(\tau,V)$ and the sound velocity $\mathscr{C}_{s}(\tau,V)$ are investigated and studied in detail. We find that the time evolution of our system is really affected by the colorlessness requirement and the initial conditions of the partonic matter: the closer the volume is to the thermodynamic limit, the longer are the times and the lifetimes of the system. A detailed analysis of the temporal decreasing, in negative power, of the energy density $\epsilon(\tau,V) \propto \tau^{-\theta}$ in each of the three stages of the Bjorken expansion is carried out.