αsdependence in the equilibration in relativistic heavy-ion collisions

The dependence of the equilibration of the parton plasma on the value of the strong coupling is studied in Au+Au collisions at LHC and at RHIC energies. With increasing coupling, the following are found to happen: (1) both thermal and chemical equilibration speed up, (2) in the final degree of equilibration, only quarks and antiquarks show obvious improvements but not gluons, and (3) the plasma cools much more rapidly. The deconfinement phase transition will therefore take place sooner and it naturally results in the shortening of the parton phase of the plasma. The exact duration of this phase is, however, sensitive to the value of the coupling. A change from ${\alpha }_s=0.3\mathrm{}$ to ${\alpha }_s=0.5\mathrm{}$, for example, reduces the lifetime of the parton phase at LHC by as much as 4.0 fm/$c$. The total generated entropy is another sensitive quantity to the coupling. Larger values of ${\alpha }_s$ will lead to entropy reduction and therefore reduction both in the duration of the mixed phase, assuming there is a first-order deconfinement phase transition, as well as in the final pion multiplicity. It is shown that the common choice of ${\alpha }_s=0.3\mathrm{}$ is not a good value for the entire duration of the evolution given that the system undergoes substantial changes from the beginning to the time that the deconfinement phase transition is about to take place assumed to be at $T_c\sim 200$ MeV. Instead, by using a more consistent simple recipe, the system is allowed to decide its own strength of the interactions which evolves with the system as it should. With this approach, ${\alpha }_s$ increases with time and this leads to acceleration in the equilibration even as equilibrium is near. This is opposite to the behavior of the equilibration of a molecular gas or ordinary many-body system where the interaction strength is fixed. In such a system, the net interactions will slow down as the system is near equilibrium.