BCS pairing in Fermi systems with N different hyperfine states

Motivated by the prospect of Bardeen-Cooper-Schrieffer (BCS) pairing in cold fermionic gases we analyze the superfluid phase of three fermionic flavors in the attractive Hubbard model. We show that there are several low-lying collective pairing modes and investigate their damping due to the partially gapless nature of the single-particle spectrum. Furthermore, we analyze how these modes show up in the density response of the system. Apart from the Anderson-Bogoliubov phase mode of the pairing between two flavors, the dynamical structure factor contains signatures of the gapless third flavor. This picture is found to be robust against perturbations that break the global SU(3) symmetry of the Hamiltonian.