BCS-BEC crossover in dense relativistic matter: Collective excitations

We study the relativistic BCS-BEC crossover within a class of Nambu-Jona-Lasinio type models, including arbitrary Lorentz-scalar pairing channels. Using the mean-field approximation we investigate spectral properties of the collective bosonic excitations in the superfluid phase, with particular attention to the Nambu-Goldstone bosons of the broken symmetry. This is a first step towards a systematic improvement of the mean-field approximation by including the fluctuation effects. The general results are illustrated on pairing in dense two-flavor quark matter-the two-flavor color superconductor.