Color-Flavor Locking and Chiral Symmetry Breaking in High Density QCD

TL;DR

This work proposes a color–flavor locked (CFL) diquark condensate in three-flavor QCD at high density, breaking $SU(3)_{color}\times SU(3)_L\times SU(3)_R\times U(1)_B$ to the diagonal $SU(3)_{color+L+R}$ and producing gaps for all quarks and gluons. Using a mean-field NJL-type model with a single-gluon-exchange–like interaction and a momentum-dependent form factor, the authors derive two coupled gap equations yielding gaps $\Delta_8$ and $\Delta_1$ whose physical manifestation is $F(\mu)^2\Delta$. Numerical results indicate plausible gaps in the 10–100 MeV range for reasonable couplings, with larger gaps possible under favorable form factors or couplings; they also predict a massless modified photon and an octet of pseudo-Nambu–Goldstone bosons, along with a singlet from baryon-number breaking. The work discusses implications for neutron star phenomenology and the QCD phase diagram, and outlines future directions, including effects of the strange quark mass, instanton-induced interactions, and beyond-mean-field treatments. Overall, the paper argues that high-density QCD could realize a robust, strongly coupled color-superconducting phase with distinctive low-energy excitations, rather than a weakly interacting quark–gluon plasma.

Abstract

We propose a symmetry breaking scheme for QCD with three massless quarks at high baryon density wherein the color and flavor SU(3)_color times SU(3)_L times SU(3)_R symmetries are broken down to the diagonal subgroup SU(3)_{color+L+R} by the formation of a condensate of quark Cooper pairs. We discuss general properties that follow from this hypothesis, including the existence of gaps for quark and gluon excitations, the existence of Nambu-Goldstone bosons which are excitations of the diquark condensate, and the existence of a modified electromagnetic gauge interaction which is unbroken and which assigns integral charge to the elementary excitations. We present mean-field results for a Hamiltonian in which the interaction between quarks is modelled by that induced by single-gluon exchange. We find gaps of order 10-100 MeV for plausible values of the coupling. We discuss the effects of nonzero temperature, nonzero quark masses and instanton-induced interactions on our results.

Figures (2)

• Figure 1: Physical color-flavor gaps as a function of chemical potential, for a smoothed-step form factor with scale $\Lambda=0.8~{\rm GeV}$ and width $w=0.05~{\rm GeV}$. The upper curve is $\Delta_1 F^2(\mu)$ while the lower curve is $\Delta_8 F^2(\mu)$. The coupling was chosen to be $\alpha = 0.252$, which is half of the coupling at which our Hamiltonian would produce a zero density chiral gap of 0.4 GeV.
• Figure 2: Color-flavor gap $\Delta_1 F(\mu)^2$ at the $\mu$ at which it is largest (solid line) and zero-density chiral gap (dashed line) as a function of coupling $\alpha$, for a smoothed-step form factor with scale $\Lambda=0.8$ and width $w=0.05~{\rm GeV}$.