  The visible and dark sectors of particle physics can be connected via kinetic
mixing between ordinary and hidden photons. If the latter is light its
production in high energy collisions of ordinary particles proceeds via
oscillations with ordinary photons similarly to the neutrino processes.
Generically, the experiments are insensitive to mass of the hidden vector, if
it is lighter than 1\,MeV, and it does not decay into $e^+e^-$-pair. Still, one
can use the missing energy and scattering off the detector material as
signatures to search for the light vectors. Presence of media suppresses
production of the light vectors making the experiments insensitive to the
entire model. We present analytic formulas for the light hidden photon
production, propagation and detection valid for searches at colliders and
beam-target experiments and apply them to estimate the impact on the
sensitivities of a set of experiments --- NA64, FASER, MATHUSLA, SHiP, T2K,
DUNE, NA62 --- in a zero-background case.
