Electron and Muon $g-2$ Constraints on Light Vector Bosons: Dark Photons and the $X_{17}$ Boson
We combine the current experimental muon $g-2$ world average, which incorporates the final Fermilab result, with the latest electron $g-2$ determinations based on cesium and rubidium measurements to set 95\% CL exclusion contours for a pure vector mediator coupled to leptons. We explicitly test the assumption that the electron and muon coupling magnitudes are equal by comparing this restricted case with the case of independent electron and muon couplings and quantify the impact on the allowed parameter space. In the minimal visible dark-photon model, both leptons constrain the same kinetic mixing and are analyzed through a combined $\chi^2$ analysis. We compare the resulting $g-2$ bounds with existing accelerator direct-search exclusions and model-dependent astrophysical and cosmological constraints. From the accelerator comparison, we identify a region in the $(m_{A'},|\epsilon|)$ parameter space near $17$~MeV, close to the reported $X_{17}$ mass, that remains allowed by the direct-search contours displayed here but is excluded by the cesium-based electron $g-2$ constraint. The rubidium-based fit does not exclude this interval. For an $X_{17}$ boson with independent lepton couplings, we constrain the electron and muon couplings separately. Electron-only direct searches leave two disconnected allowed regions near the reported $X_{17}$ mass: a newly reopened low-coupling interval and a higher-coupling region above the NA64 excluded band. The cesium-based electron $g-2$ constraint closes the higher-coupling region, while the rubidium-based constraint reduces its extent; neither affects the newly reopened low-coupling interval. Using the current experimental muon $g-2$ world average, we obtain a new $g-2$-based exclusion region for the muon coupling, with no significant preference for a nonzero coupling.