  We leverage random phase approximation and unbiased auxiliary-field quantum
Monte Carlo methods to compute dynamical correlations for a dilute homogeneous
two-dimensional attractive Fermi gas. Our main purpose is to quantitatively
study the collective excitations of the system to generate robust benchmark
results and to shed light into fermionic superfluidity in the strongly
correlated regime. In particular we are motivated by a recent paper suggesting
that the Higgs mode can be detected in the spectrum of spin fluctuations.
Despite the fact that we are somewhat limited by finite-size effects, our study
pinpoints indeed a clear peak in the spin channel at low momentum, but a
detailed analysis suggests that such a peak, though certainly interesting, does
not correspond to the Higgs mode. We propose a different explanation for the
shape of the spin structure factor. On the other hand, our results clearly show
that the Higgs mode can be detected in the density channel at very small wave
vectors, although very good resolution is necessary.
