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

Abstract

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 quantum chromodynamics 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 Relativistic Heavy Ion Collider energies. We show that for a standard choice of parameters, this ratio reaches 1, though the maximum is very sensitive to the initial evolution proper time.