Thomas-Fermi Statistical Models of Finite Quark Matter

TL;DR

This paper introduces a Thomas-Fermi statistical model for finite quark matter, capturing confinement and residual color Coulomb attraction, with applications to baryonic states and potential extensions to multi-meson systems.

Contribution

It presents a novel application of the Thomas-Fermi model to finite quark matter, including confinement effects and baryonic applications, advancing understanding of multi-quark phenomenology.

Findings

Bound states arise from residual color Coulomb attraction without explicit confinement terms.

The model applies to nonrelativistic and ultra-relativistic baryonic states, including color-flavor locking.

Potential extensions to multi-meson and mixed hadronic states are discussed.

Abstract

I introduce and discuss models of finite quark matter using the formalism of the Thomas-Fermi statistical model. Similar to bag models, a vacuum energy term is introduced to model long distance confinement, but the model produces bound states from the residual color Coulomb attraction even in the absence of such a term. I discuss three baryonic applications: an equal mass nonrelativistic model with and without volume pressure, the ultra-relativistic limit confined by volume pressure, and a color-flavor locking massless model. These model may be extended to multi-meson and other mixed hadronic states. Hopefully, it can help lead to a better understanding of the phenomenology of high multi-quark states in preparation for more detailed lattice QCD calculations.