Asymptotic freedom and the baryon-quark phase transition

Abstract

We have calculated the ground-state properties of a quark gas to second order in the quark-gluon coupling constant. Asymptotic freedom has been taken into account by using the renormalized coupling constant of Politzer and Gross and Wilczek. We find that this asymptotically free perturbation theory leads to an equation of state for a quark gas which for pressure $P>\mathrm{}0\mathrm{}$ is very similar to the equation of state obtained from the MIT bag model of hadrons. In particular, we can identify a "bag pressure" term in the perturbation theory expression for the pressure as a function of density. We obtain estimates for the baryonquark transition pressure by comparing the perturbation theory results with the Gibbs energy per baryon of baryonic matter. Our calculations show that the baryon-quark transition takes place at densities on the order of 10-20 times that in ordinary nuclei. These transition densities are higher than the maximum central density calculated for a neutron star.