Chemical Equilibration in Relativistic Heavy Ion Collisions

In the hadronic sector of relativistic heavy ion physics, the $\rho <=> 2\pi$ reaction is the strongest one, strong enough to equilibrate the $\rho$ with the pions throughout the region from chemical freezeout to thermal freezeout when free-particle interactions (with no medium-dependent effects) are employed. Above the chiral restoration temperature, only $\rho$'s and $\pi$'s are present, in that the chirally restored $A_1$ is equivalent to the $\rho$ and the mesons have an SU(4) symmetry, with no dependence on isospin and negligible dependence on spin. In the same sense the $\sigma$ and $\pi$ are "equivalent" scalars. Thus the chirally restored $\rho\leftrightarrows 2\pi$ exhaust the interspecies transitions. We evaluate this reaction at $T_c$ and find it to be much larger than below $T_c$, certainly strong enough to equilibrate the chirally restored mesons just above $T_c$. When emitted just below $T_c$ the mesons remain in equilibrium, at least in the chiral limit because of the Harada-Yamawaki "vector manifestation" that requires that mesonic coupling constants go to zero (in the chiral limit) as $T$ goes to $T_c$ from below. Our estimates in the chiral limit give deviations in some particle ratios from the standard scenario (of equilibrium in the hadronic sector just below $T_c$) of about double those indicated experimentally. This may be due to the neglect of explicit chiral symmetry breaking in our estimates. We also show that the instanton molecules present above $T_c$ are the giant multipole vibrations found by Asakawa, Hatsuda and Nakahara and of Wetzorke et al. in lattice gauge calculations. Thus, the matter formed by RHIC can equivalently be called: chirally restored mesons, instanton molecules, or giant collective vibrations. It is a strongly interacting liquid.