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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 (mₕ-) parameter space. We point out that mₕ214 MeV and ^2>310^-5 can be consistent with the hypothesis of the HyperCP Collaboration, which seeks to explain the anomalous energy distribution of muon pairs in the ^+^+^- process by a resonance, without direct contradiction to the existing data on radiative kaon decays. The same parameters lead to an O (few10^-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^-^+^- cross section and dedicated analysis of lepton spectra from K^+^+e^+e^- decays should be able to provide a conclusive test of this hypothesis and improve the constraints on the model.
Maxim Pospelov (Mon,) studied this question.