  We examine the production of an invisible state $X$ together with a photon,
$e^+e^- \to \gamma +X$, at electron positron colliders and present measurement
strategies that can detect the spin of the invisible state as well as the
underlying production mechanism, based on the angular distribution of the final
state photon, the cross sections for polarized initial states and the photon
polarization. Our measurement strategy can be used to identify whether the
invisible state is a hidden photon or an axion. The results are compared with a
detailed analysis of the Standard Model background and we calculate the
sensitivity reach for searches for axions and hidden photons at Belle II.
