  Kinetic mixing of the dark photon, the gauge boson of a hidden $U(1)_D$, with
the Standard Model (SM) gauge fields to induce an interaction between ordinary
matter and dark matter (DM) at 1-loop requires the existence of portal matter
(PM) fields having both dark and SM charges. As discussed in earlier work,
these same PM fields can also lead to other loop-level mechanisms besides
kinetic mixing that can generate significant interactions between SM fermions
and the dark photon in a manner analogous to those that can be generated
between a Dirac neutrino and a SM photon, \ie, dark moments. In either case,
there are reasons to believe, \eg, due to the RGE running of the $U(1)_D$ gauge
coupling, that PM fields may have $\sim$ TeV-scale masses that lie at or above
those directly accessible to the HL-LHC. If they lie above the reach of the
HL-LHC, then the only way to possibly explore the physics at this high scale in
the short term is via indirect measurements made at lower energies, \eg, at
lepton colliders operating in the $m_Z$ to 1 TeV range. In particular,
processes such as $e^+e^- \to \gamma+$DM or $e^+e^-\to \bar ff$, where $f$ is a
SM fermion, may be most useful in this regard. Here we explore these
possibilities within the framework of a simple toy PM model, introduced in
earlier work, based on a non-abelian dark gauge group completion operating at
the PM scale. In the KM setup, we show these efforts fail due to the inherently
tiny cross sections in the face of substantial SM backgrounds. However, in the
case of interactions via induced dark moments, since they necessarily take the
form of higher dimensional operators whose influence grows with energy, we show
that access to PM-scale information may become possible for certain ranges of
the toy model parameters for both of these $e^+e^-$ processes at a 1 TeV
collider.
