  Out-of-equilibrium quasistationary states (QSSs) are one of the signatures of
a broken ergodicity in long-range interacting systems. For the widely studied
Hamiltonian Mean-Field model, the lifetime of some QSSs has been shown to
diverge with the number N of degrees of freedom with a puzzling N^1.7 scaling
law, contradicting the otherwise widespread N scaling law. It is shown here
that this peculiar scaling arises from the locality properties of the dynamics
captured through the computation of the diffusion coefficient in terms of the
action variable. The use of a mean first passage time approach proves to be
successful in explaining the non-trivial scaling at stake here, and sheds some
light on another case, where lifetimes diverging as e^N above some critical
energy have been reported.
