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 ($ψ$) and a heavy quark ($Ψ$). We introduce a gap function $Δ\sim \langle \bar ψΨ\rangle $ which represents the correlation between $ψ$ and $Ψ$, and perform the mean-field approximation assuming that heavy quarks are uniformly distributed. Values of the gap $Δ$ measure the strength of mixing between $ψ$ and $Ψ$. 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 $μ$ (the light-quark chemical potential) and $λ$ (an analog of the heavy-quark chemical potential) plane, and identify the region where the QCD Kondo effect occurs.