Functional Renormalization Group analysis of the quark-condensation pattern on the Fermi surface: A simple effective-model approach

Abstract

A simple effective model for the intermediate-density regime is constructed from the high-density effective theory of quantum chromodynamics (QCD). In the effective model, under a renormalization-group (RG) scaling towards low momenta, the original QCD interactions lead to four-quark contact interactions for the relevant quark and hole modes around the Fermi surface. The contact interaction in the scalar channel can be traced back to zero-sound-type collinear quark scattering near the Fermi surface in an instanton background. The quark and hole states in opposite directions of a given Fermi velocity form the collective scalar bosonic mode $\ddot{I}ƒ$. The magnitude of $\ddot{I}ƒ$ is investigated via the non-perturbative Functional Renormalization Group (FRG) evolution of the effective average action from the ultraviolet (UV) to the infrared (IR). In the mean background-field approximation for $\ddot{I}ƒ$, nontrivial minima ($\bar{\ddot{I}}ƒ\ne 0$) are found in the IR limit of the effective average action. A nonvanishing $\bar{\ddot{I}}ƒ$ corresponds to condensation of quark and hole states in opposite directions of a given Fermi velocity, in a thin shell-like structure in momentum space around the Fermi surface. This looks similar to the shell-like baryon distribution in momentum space assumed in the quarkyonic-matter concept. However, when including a dynamic bosonic $\ddot{I}ƒ$-mode in the RG flow, we find that its diffusive nature destroys the quark-hole condensate, i.e., the IR potential does not show any minima beyond the trivial one.

27 pages, 11 figures