  We show that in the equilibrium phase of glass-forming hard-sphere fluids in
three dimensions, the static length scales tentatively associated with the
dynamical slowdown and the dynamical length characterizing spatial
heterogeneities in the dynamics unambiguously decorrelate. The former grow at a
much slower rate than the latter when density increases. This observation is
valid for the dynamical range that is accessible to computer simulations, which
roughly corresponds to that of colloidal experiments. We also find that in this
same range, no one-to-one correspondence between relaxation time and
point-to-set correlation length exists. These results point to the coexistence
of several relaxation mechanisms in the accessible dynamical regime of
three-dimensional hard-sphere glass formers.
