Gapless Color-Flavor-Locked Quark Matter

Abstract

In neutral cold quark matter that is sufficiently dense that the strange quark mass M_s is unimportant, all nine quarks (three colors; three flavors) pair in a color-flavor locked (CFL) pattern, and all fermionic quasiparticles have a gap. We argue that as a function of decreasing quark chemical potential mu or increasing M_s, there is a quantum phase transition from the CFL phase to a new ``gapless CFL phase'' in which only seven quasiparticles have a gap. The transition occurs where M_s^2/mu is approximately equal to 2*Delta, with Delta the gap parameter. Gapless CFL, like CFL, leaves unbroken a linear combination Qtilde of electric and color charges, but it is a Qtilde-conductor with a nonzero electron density. These electrons and the gapless quark quasiparticles make the low energy effective theory of the gapless CFL phase and, consequently, its astrophysical properties are qualitatively different from those of the CFL phase, even though its U(1) symmetries are the same. Both gapless quasiparticles have quadratic dispersion relations at the quantum critical point. For values of M_s^2/mu above the quantum critical point, one branch has conventional linear dispersion relations while the other branch remains quadratic, up to tiny corrections.