Lepton Phenomenology of Stueckelberg Portal to Dark Sector

We propose an extension of the Standard Model (SM) with a $U_{A'}(1)$ gauge invariant dark dector connected to the SM via a new portal -- the Stueckelberg portal, arising in the framework of dark photon $A'$ mass generation via Stueckelberg mechanism. This portal opens through the effective dim=5 operators constructed from the covariant term of the auxiliary Stueckelberg scalar field $\sigma$ providing flavor non-diagonal renormalizable couplings of both $\sigma$ and $A'$ to the SM fermions $\psi$. The Stueckelberg scalar plays a role of Goldstone boson in the generation of mass of the Dark Photon. Contrary to the conventional kinetic mixing portal, in our scenario flavor diagonal $A'$-$\psi$ couplings are not proportional to the fermion charges and are, in general, flavor nondiagonal. These features drastically change the phenomenology of dark photon $A'$ relaxing or avoiding some previously established experimental constraints. We focus on the phenomenology of the described scenario of the Stueckelberg portal in the lepton sector and analyze the contribution of the dark sector fields $A'$ to the anomalous magnetic moment of muon $(g-2)_{\mu}$, lepton flavor violating decays $l_{i}\to l_{k}\gamma$ and $\mu-e$ conversion in nuclei. We obtain limits on the model parameters from the existing data on the corresponding observables.