Kondo phase diagram of quark matter

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.