  We analyze the effects of order parameter fluctuations on the ground state of
fully gapped charge-neutral fermionic superfluids. The Goldstone mode
associated with the spontaneously broken symmetry leads to a problem of coupled
singularities in $d \leq 3$ dimensions. We derive a minimal set of one-loop
renormalization group equations which fully captures the interplay of the
singularities. The flow equations are based on a symmetry conserving truncation
of a scale dependent effective action. We compute the low energy behavior of
longitudinal, transverse and mixed order parameter correlations, and their
impact on the fermionic gap. We demonstrate analytically that cancellations
protecting the Goldstone mode are respected by the flow, and we present a
numerical solution of the flow equations for the two-dimensional attractive
Hubbard model.
