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 Sector connected to the SM via a new portal arising in the framework of dark photon $A'$ mass generation via Stueckelberg mechanism. This mechanism implies the existence of a scalar field $\sigma$, which is shift-transformed under this group and resembles an axion-like particle (ALP) widely addressed in the literature in different contexts. The effective dim=5 operators constructed of the covariant derivative of the $\sigma$ field generate flavor non-diagonal renormalizable couplings of both $\sigma$ and $A'$ to the SM fermions $\psi$. Contrary to the conventional kinetic mixing portal, in our scenario flavor diagonal $A'$-$\psi$ couplings are not proportional to the fermion charges. 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 $A'$ and $\sigma$ 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 experimental data on the corresponding observables.