Quarkyonic Mean Field Theory

TL;DR

This paper develops a mean field theory model of Quarkyonic matter at zero temperature, describing nucleons and quarks with specific interactions, and proposes a phenomenological equation of state for the transition between hadronic and quark phases.

Contribution

It introduces a dual description of Fermi sea occupation in Quarkyonic matter and models the transition using a phenomenological approach with simplified interactions.

Findings

A model for the phase transition in Quarkyonic matter is proposed.

Quark and nucleon interactions are simplified to vector interactions, with a phenomenological relation for quark Fermi energy.

The theory provides a framework for understanding low to high density matter in QCD.

Abstract

We discuss mean field theory of Quarkyonic matter at zero temperature. We treat the nucleons with contact interactions in mean field approximation, discussing both vector and scalar mean field interactions. We treat the quarks without mean field vector interactions, but allow mass terms to be generated consistent from a scalar mean field consistent with the additive quark model for quark masses. Quarkyonic matter is composed of a shell of nucleons that under-occupy the total available phase space associated with the underlying quark degrees of freedom. The fully occupied Fermi sphere beneath this shell of nucleons at high densities is thought of as quarks, but when this fully occupied distribution of states first appears, although the phase space is filled, the matter is at low density. For the transition between this low density and high density saturated matter, we advocate a dual description of the fully filled Fermi sea in terms of hadrons, and make a phenomenological hypothesis for the equation of state of this matter. We then proceed to an example where the mean field interactions are all vector and only associated with the nucleons, ignoring the effects of mass change associated with the scalar interactions. Except for the effects of Pauli blocking, the nucleons and quarks do not interact. To get a reasonable transition to Quarkyonic matter the interaction of the quarks among themselves are assumed to be non-perturbative, and a simple phenomenological relation between quark Fermi energy and density is introduced.