Proposal to search for a dark photon in $e^+$ on target collisions at DA$Φ$NE linac

Photon-like particles are predicted in many extensions of the Standard Model. They have interactions similar to the photon, are vector bosons, and can be produced together with photons. The present paper proposes a search for such particles in the $ e^+e^- \to U\gamma$ process in a positron-on-target experiment, exploiting the positron beam of the DA$\Phi$NE LINAC at the Laboratori Nazionali di Frascati, INFN. With a 550 MeV/c beam and $10^4$ positrons per bunch in one year of running a sensitivity in the relative coupling constant down to $10^{-6}$ is achievable, in the mass region from 2.5 MeV$<M_U<$ 20 MeV, compatible with the preferred region from the 3$\sigma$ discrepancy in $g_{\mu} -2$. The proposed experimental setup and the analysis technique is discussed