  Electron positron collisions are a very promising environment to search for
new physics, and in particular for dark sector related observables. The most
challenging experimental problem in detecting dark sector candidates is the
very high associated Standard Model background. For this reason it is important
to identify observables that are, at the same time, minimally suppressed in the
dark sector and highly suppressed in the Standard Model. One example is the
$e^+ e^-\to 3(e^+e^-)$ process that can be mediated either by the production
and subsequent decay of dark Higgs ($h'$), $e^+e^-\to A'h'\to 6e$ or produced
by the Standards Model process $e^+ e^-\to 3(e^+e^-)$. In the following letter
we study the relative contribution to observed $e^+ e^-\to 3(e^+e^-)$ total
cross section, coming from the $h'$ mediated and from the Standard Model
processes in the contest of fixed target and low energy collider experiments,
with particular attention to the PADME experiment at the INFN Laboratori
Nazionali di Frascati.
