Collective excitations in a superfluid of color-flavor locked quark matter

We investigate collective excitations coupled with baryon density in a system of massless three-flavor quarks in the collisionless regime. By using the Nambu-Jona-Lasinio (NJL) model in the mean-field approximation, we field-theoretically derive the spectra both for the normal and color-flavor locked (CFL) superfluid phases at zero temperature. In the normal phase, we obtain usual zero sound as a low-lying collective mode in the particle-hole (vector) channel. In the CFL phase, the nature of collective excitations varies in a way dependent on whether the excitation energy, ω, is larger or smaller than the threshold given by twice the pairing gap Δ, at which pair excitations with nonzero total momentum become allowed to break up into two quasiparticles. For ω<<2Δ, a phonon corresponding to fluctuations in the U(1) phase of Δ appears as a sharp peak in the particle-particle ('H') channel. We reproduce the property known from low-energy effective theories that this mode propagates at a velocity of vH=1/√(3) in the low momentum regime; the decay constant fH obtained in the NJL model is identical with the QCD result obtained in the mean-field approximation. We also find that, as the momentum of the phonon increases, the excitation energy goes up and asymptotically approaches ω=2Δ. Above the threshold for pair excitations (ω>2Δ), zero sound manifests itself in the vector channel. By locating the zero sound pole of the vector propagator in the complex energy plane, we investigate the attenuation and energy dispersion relation of zero sound. In the long wavelength limit, the phonon mode, the only low-lying excitation, has its spectral weight in the H channel alone, while the spectral function vanishes in the vector channel. This is due to nontrivial mixing between the H and vector channels in the superfluid medium. We finally extend our study to the case of nonzero temperature. We demonstrate how Landau damping smears the phonon peak in the finite temperature spectral function. We find a pure imaginary pole of the H propagator in the complex energy plane, which can be identified as a diffusive mode responsible for the Landau damping. From the pole position we derive the thermal diffusion constant