Secluded U(1) below the weak scale

Abstract

A secluded U(1) sector with weak admixture to photons, $O({10}^{\ensuremath{-}2}\ensuremath{-}{10}^{\ensuremath{-}3})$, and the scale of the breaking below 1 GeV represents a natural yet poorly constrained extension of the standard model. We analyze $g\ensuremath{-}2$ of muons and electrons together with other precision QED data, as well as radiative decays of strange particles to constrain the mass-mixing angle (${m}_{V}\ensuremath{-}\ensuremath{\kappa}$) parameter space. We point out that ${m}_{V}\ensuremath{\simeq}214\text{ }\text{ }\mathrm{MeV}$ and ${\ensuremath{\kappa}}^{2}>3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ can be consistent with the hypothesis of the HyperCP Collaboration, which seeks to explain the anomalous energy distribution of muon pairs in the ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ process by a resonance, without direct contradiction to the existing data on radiative kaon decays. The same parameters lead to an $O(\mathrm{\text{few}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9})$ upward correction to the anomalous magnetic moment of the muon, possibly relaxing some tension between the experimental value and theoretical determinations of $g\ensuremath{-}2$. The ultrafine energy resolution scan of the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ cross section and dedicated analysis of lepton spectra from ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{e}^{+}{e}^{\ensuremath{-}}$ decays should be able to provide a conclusive test of this hypothesis and improve the constraints on the model.