Kondo phase diagram of quark matter

TL;DR

This paper explores the phase diagram of quark matter with heavy quark impurities, demonstrating the conditions under which the QCD Kondo effect occurs through a mean-field analysis of a simplified interaction model.

Contribution

It introduces a mean-field framework to analyze the Kondo effect in quark matter, mapping out the phase diagram based on chemical potentials and identifying the Kondo region.

Findings

Nonzero gap solutions indicate the Kondo effect in certain parameter regions.

The phase diagram delineates the Kondo and non-Kondo phases.

The model predicts the stability of the Kondo phase under specific conditions.

Abstract

We discuss the ground state of a quark matter containing heavy quarks as impurities in a simple model which exhibits the QCD Kondo effect. The model includes a current-current interaction with the color exchange between a light quark ($\psi$) and a heavy quark ($\Psi$). We introduce a gap function $\Delta \sim \langle \bar \psi \Psi \rangle $ which represents the correlation between $\psi$ and $\Psi$, and perform the mean-field approximation assuming that heavy quarks are uniformly distributed. Values of the gap $\Delta$ measure the strength of mixing between $\psi$ and $\Psi$. The gap equation obtained from the minimum of the thermodynamical potential together with the condition for the heavy-quark number conservation turns out to allow for nonzero values of the gap as the most stable state. We draw a phase diagram in $\mu$ (the light-quark chemical potential) and $\lambda$ (an analog of the heavy-quark chemical potential) plane, and identify the region where the QCD Kondo effect occurs.