  We develop an effective field theory to understand collective modes of a
three-dimensional two-component Fermi superfluid with dipolar inter-particle
interactions, which are modeled by an idealized separable potential. We first
examine the phase transition of the system at zero temperature, as the
fermionic superfluidity is known to be characterized by two competing order
parameters. We find that for strong interactions there exists a regime where
the two order parameters are out-of-phase and coupled, giving rise to an
undamped massive Leggett mode. This is in addition to the well-known gapless
phonon mode. We show that the Leggett mode can be seen in the spectral function
of the in-medium Cooper pairs, and in principle could be measured through Bragg
spectroscopy.
