Superfluid phases of quark matter, II: Phenomenology and sum rules

Abstract

We derive sum rules for a uniform, isotropic superfluid quark-gluon plasma with massless quarks, first laying out the phenomenological equations obeyed by a color superconductor in terms of macroscopic observables such as the superfluid mass and baryon densities, and the electric and magnetic gluon masses, and then expressing these quantities in terms of equilibrium correlation functions. From the transverse part of the long wavelength baryon current-momentum correlation function we derive an exact expression for the superfluid baryon density, and from the longitudinal part, an f-sum rule. From the transverse part of the long wavelength color current-current correlation function we derive the superfluid Meissner mass, and from the longitudinal part, the Debye mass. These masses constrain integrals of the transverse and longitudinal parts of the gluon propagator over frequencies, and provide self-consistent conditions for a solution to the gap equation beyond weak coupling.