  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 mass--mixing angle (m_V-\kappa) parameter
space. We point out that m_V = 214 MeV and \kappa^2 > 3\times 10^{-5} can be
consistent with the hypothesis of HyperCP collaboration, that seeks to explain
the anomalous energy distribution of muon pairs in the \Sigma^+ \to p
\mu^+\mu^- process by a resonance, without direct contradiction to the existing
data on radiative kaon decays. The same parameters lead to O({\rm few} \times
10^{-9}) upward correction to the anomalous magnetic moment of the muon,
possibly relaxing some tension between experimental value and theoretical
determinations of g-2. The ultra-fine energy resolution scan of e^+e^-\to
\mu^+\mu^- cross section and dedicated analysis of lepton spectra from K^+\to
\pi^+ e^+e^- decays should be able to provide a conclusive test of this
hypothesis and improve the constraints on the model.
