Chiral Symmetry Breaking in High Density QCD

We propose a symmetry breaking scheme for QCD with three massless quarks at high baryon density wherein the color and flavor SU(3)color×SU(3)L×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 hundreds of MeV for plausible values of the coupling. We discuss the effects of nonzero temperature, nonzero quark masses and instanton-induced interactions on our results.