Collective modes in the color flavor locked phase

TL;DR

This paper analyzes the low energy collective excitations in the color flavor locked phase of QCD, focusing on the Higgs and Nambu-Goldstone modes, using the Nambu-Jona Lasinio model to derive their effective interactions.

Contribution

It provides a detailed derivation of the effective action for collective modes, including corrections due to the gap, and explores interactions between Higgs and Nambu-Goldstone fields.

Findings

Derived the effective Lagrangian for Nambu-Goldstone modes.

Evaluated corrections to the Goldstone mode due to the gap.

Determined interaction terms between Higgs and Goldstone modes.

Abstract

We study the low energy effective action for the collective modes of the color flavor locked phase of QCD. This phase of matter has long been known to be a superfluid because by picking a phase its order parameter breaks the quark-number $U(1)_B$ symmetry spontaneously. We consider the modes describing fluctuations in the magnitude of the condensate, namely the Higgs mode, and in the phase of the condensate, namely the Nambu-Goldstone (or Anderson-Bogoliubov) mode associated with the breaking of $U(1)_B$. By employing as microscopic theory the Nambu-Jona Lasinio model, we reproduce known results for the Lagrangian of the Nambu-Goldstone field to the leading order in the chemical potential and extend such results evaluating corrections due to the gap parameter. Moreover, we determine the interaction terms between the Higgs and the Nambu-Goldstone field. This study paves the way for a more reliable study of various dissipative processes in rotating compact stars with a quark matter core in the color flavor locked phase.