The long standing problem of reconciling the cosmological evidence for the existence of dark matter with the lack of any clear experimental observation of it, has recently revived the idea that the new particles are neutral under the Standard Model (SM) gauge interactions, and only mediator fields or "portals", connect our world with new "secluded" or "hidden" sectors. One of the simplest models just adds an additional $U(1)$ symmetry, with its corresponding vector boson, $A'$.

All SM particles will be neutral under this symmetry, while the new field will couple to the charged particles of the SM with an effective charge $\varepsilon e$, so that this new particle is often called "dark photon". Additional interest arises from the observation that $A'$ in the mass range 1 MeV$/c^2$ to 1 GeV$/c^2$ and coupling $\varepsilon\sim10^{-3}$, would justify the discrepancy between theory and observation for the muon anomalous magnetic moment, $(g-2)_\mu$. This possibility has been recently disproved in the hypothesis that the $A'$ decays to SM particles only, on the contrary if $A'$ decays to dark sector particles, almost all of the available experimental constraints can be evaded and the dark photon is still a viable explanation for the $(g-2)_\mu$ anomaly.

Due to the weak experimental signature, the search for invisibly decaying $A'$ requires a carefully designed dedicated experiment: at the end of 2015 INFN has approved PADME, searching for invisible decays of the $A'$ at the DA$\Phi$NE LINAC in Frascati. The experiment is designed for detecting dark photons produced by the annihilation of a 550 MeV positron beam onto a thin target, by measuring the final state missing mass by reconstructing only the recoiling photon in $e^+e^-\to A' \gamma$ events, regardless of the decay channel of the $A'$. The collaboration aims at completing the costruction by the end of 2017 and collecting $\approx 10^{13}$ positrons on target by the end of 2018, in order to reach a sensitivity at the level of $10^{-3}$ for $\varepsilon$, up to a dark photon mass of <23 MeV$/c^2$.