Electron-muon conversion in nuclei and rare decays induced by LFV dark photon

We study lepton-flavor violation (LFV) effects occurring in the $e-\mu$ conversion in nuclei and in the rare radiative decays $\eta ({\eta }^{\mathrm{\prime }})\to \gamma \mu e$ of the $\eta$ and ${\eta }^{\mathrm{\prime }}$ mesons with a special impact of the sub-GeV mass vector mediator (dark photon). In the case of the lepton conversion, we make estimates for running and future experiments operating with electron beams at fixed target. Obtained results are implemented in analysis of the LFV decays $\eta ({\eta }^{\mathrm{\prime }})\to \gamma \mu e$.