  We study portal interactions connecting visible and dark sectors, and
involving local interactions of a photon, a dark photon and a axion-like
particle (ALP) at future $e^+e^-$ colliders. These interactions, mediated by
higher-dimensional effective operators, may arise at one-loop by kinetic mixing
between dark and ordinary photons, or, for massless dark photons, by direct
short-distance contributions. We explore these portal interactions for a heavy
ALP with masses between about 10 GeV and 230 GeV by investigating the
sensitivity of the production $e^+e^- \to \gamma \gamma \bar{\gamma}$ to the
effective couplings, where the dark photon $\bar\gamma$ gives rise to missing
momentum in the final state. We will show how an appropriate choice of
missing-energy and missing-mass cuts can optimize the signal to standard-model
background ratio. Exclusion regions for the effective photon-dark-photon-ALP
couplings versus the ALP mass are worked out for a few representative values of
the collision energy and integrated luminosity, as presently envisaged by
future $e^+e^-$ projects.
