How does color neutrality affect collective modes in color superconductors?

TL;DR

This paper investigates how imposing color neutrality constraints affects collective excitations in color superconductors, demonstrating that Nambu-Goldstone bosons remain massless and analyzing their dispersion relations.

Contribution

It clarifies the role of color neutrality in collective modes, showing that Nambu-Goldstone bosons stay massless and coupling to charge density fluctuations is properly accounted for.

Findings

Nambu-Goldstone bosons remain massless under color neutrality.

Proper generalization of neutrality constraints is essential for consistent collective mode analysis.

Effective field theory and high-density approximation are used to derive dispersion relations.

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.