Restrained Dark $U(1{)}_d$ at Low Energies

Abstract

We investigate a spontaneously broken $U(1{)}_d$ gauge symmetry with a muon-specific dark Higgs. Our first goal is to verify how the presence of a new dark Higgs, $\varphi$, and a dark gauge boson, $V$, can simultaneously face the anomalies from the muon magnetic moment and the proton charge radius. Secondly, by assuming that $V$ must decay to an electron-positron pair, we explore the corresponding parameter space determined with the low energy constraints coming from $K\to \mu X$, electron $(g-2{)}_e$, $K\to \mu {\nu }_{\mu }{e}^{+}{e}^{-}$, $K\to \mu {\nu }_{\mu }{\mu }^{+}{\mu }^{-}$, $\tau \to {\nu }_{\tau }\mu {\nu }_{\mu }{e}^{+}{e}^{-}$. We focus in the scenario where the $V$ mass is below $\sim 2m_{\mu }$ and the $\varphi$ mass runs from few MeV till $250$ MeV, with V-photon mixing of the order $\sim \mathcal{O}(10^{-3})$. Among weak process at low energies, we check the influence of the new light vector on kaon decays as well as on the scattering $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}{e}^{+}{e}^{-}$ and discuss the impact of the dark Higgs on $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$. Finally, we consider contributions of the V-photon mixing in the decays ${\pi }^0\to \gamma e^{+}{e}^{-}$, $\eta \to \gamma e^{+}{e}^{-}$, $\rho \to \pi e^{+}{e}^{-}$, $K^{\ast }\to K{e}^{+}{e}^{-}$ and $\varphi (1020)\to \eta e^{+}{e}^{-}$.

arXiv comment13 pages, 10 figures

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