Dynamical quark recombination in ultrarelativistic heavy-ion collisions and the proton to pion ratio

We study quark thermal recombination as a function of energy density during the evolution of a heavy-ion collision in a numerical model that reproduces aspects of QCD phenomenology. We show that starting with a set of free quarks (or quarks and antiquarks) the probability to form colorless clusters of three quarks differs from that to form colorless clusters of quark-antiquark and that the former has a sharp jump at a critical energy density whereas the latter transits smoothly from the low to the high energy density domains. We interpret this as a quantitative difference in the production of baryons and mesons with energy density. We use this approach to compute the proton and pion spectra in a Bjorken scenario that incorporates the evolution of these probabilities with energy density, and therefore with proper time. From the spectra, we compute the proton to pion ratio and compare to data at the highest RHIC energies. We show that for a standard choice of parameters, this ratio reaches one, though the maximum is very sensitive to the initial evolution proper time.