  In this article we investigate the properties of an impurity immersed in a
superfluid of strongly correlated spin 1/2 fermions. For resonant interactions,
we first relate the stability diagram of dimer and trimer states to the
three-body problem for an impurity interacting with a pair of fermions. Then we
calculate the beyond-mean-field corrections to the energy of a weakly
interacting impurity. We show that these corrections are divergent and have to
be regularized by properly accounting for three-body physics in the problem.
