Secluded U(1) below the weak scale

A secluded U(1) sector with weak admixture to photons, O(10^-2-10^-3), and the scale of the breaking below 1 GeV represents a natural yet poorly constrained extension of the standard model. We analyze g-2 of muons and electrons together with other precision QED data, as well as radiative decays of strange particles to constrain the mass-mixing angle (mV-κ) parameter space. We point out that mV214 MeV and κ²>3×10^-5 can be consistent with the hypothesis of the HyperCP Collaboration, which seeks to explain the anomalous energy distribution of muon pairs in the Σ⁺→pμ⁺μ^- process by a resonance, without direct contradiction to the existing data on radiative kaon decays. The same parameters lead to an O(few×10^-9) upward correction to the anomalous magnetic moment of the muon, possibly relaxing some tension between the experimental value and theoretical determinations of g-2. The ultrafine energy resolution scan of the e⁺e^-→μ⁺μ^- cross section and dedicated analysis of lepton spectra from K⁺→π⁺e⁺e^- decays should be able to provide a conclusive test of this hypothesis and improve the constraints on the model.