Thermodynamics of confined quarks

Abstract

We investigate the thermodynamics of strongly interacting matter described as a system of quarks and antiquarks in free creating and annihilation, but with pairwise confinement to a volume of hadronix size ($\ensuremath{\sim}\frac{4\ensuremath{\pi}}{3{{m}_{\ensuremath{\pi}}}^{3}}$). At low temperature, such a system behaves like a hadron gas, giving a quark or an antiquark a spatial mobility of order ${{m}_{\ensuremath{\pi}}}^{\ensuremath{-}1}$. At high temperature and hence high density, we obtain a gas of free quarks and antiquarks with infinite spatial mobility. By calculating the crossover of low- and high-temperature approximations, we find a phase transition from hadron to quark matter at the critical temperature ${T}_{c}\ensuremath{\simeq}{m}_{\ensuremath{\pi}}$. We compare our results with similar considerations based on the size of hadrons and on perturbative quantum chromodynamics.