How does color neutrality affect collective modes in color superconductors?

Abstract

We revisit the issue of color neutrality in effective model descriptions of dense quark matter based on global color symmetry. While the equilibrium thermodynamics of such models is now well understood, we examine the collective modes, focusing on the fluctuations of the order parameter. We point out that the constraint of color neutrality must be carefully generalized in order to obtain physically consistent and well-defined results. Particularly important is that the collective modes associated with order parameter fluctuations couple to charge density fluctuations in the neutral medium. We start by proving explicitly that, in contrast to claims made previously in literature, Nambu-Goldstone bosons of spontaneously broken global color symmetry remain exactly massless even after imposing the color neutrality constraint. As the next step, we make the argument general by using effective field theory. We then employ the high-density approximation to calculate the couplings in the effective Lagrangian and thus the Nambu-Goldstone boson dispersion relations.