Lepton flavor violation and scotogenic Majorana neutrino mass in a Stueckelberg $U(1)_X$ model

Abstract

We construct a scotogenic Majorana neutrino mass model in a gauged $U(1)_X$ extension of the standard model, where the mass of the gauge boson and the unbroken gauge symmetry, which leads to a stable dark matter (DM), can be achieved through the Stueckelberg mechanism. It is found that the simplest version of the extended model consists of the two inert-Higgs doublets and one vector-like singlet fermion. In addition to the Majorana neutrino mass, we study the lepton flavor violation (LFV) processes, such as $\ell_i \to \ell_j \gamma$, $\ell_i \to 3 \ell_j$, $\mu-e$ conversion rate in nucleus, and muonium-antimuonium oscillation. We show that the sensitivities of $\mu\to 3e$ and $\mu-e$ conversion rate designed in Mu3e and COMET/Mu2e experiments make both decays the most severe constraints on the $\mu\to e$ LFV processes. It is found that $\tau\to \mu \gamma$ and $\tau\to 3\mu$ can reach the designed significance level of Belle II. In addition to explaining the DM relic density, we also show that the DM-nucleon scattering cross section can satisfy the currently experimental limit of DM direct detection.