Search for the dark photon and the dark Higgs boson at Belle

Abstract

The dark photon, $A^{\prime }$, and the dark Higgs boson, $h^{\prime }$, are hypothetical constituents featured in a number of recently proposed Dark Sector Models. Assuming prompt decays of both dark particles, we search for their production in the so-called Higgs-strahlung channel, $e^{+}{e}^{-}\to A^{\prime }{h}^{\prime }$, with $h^{\prime }\to A^{\prime }{A}^{\prime }$. We investigate ten exclusive final-states with $A^{\prime }\to e^{+}{e}^{-}$, ${\mu }^{+}{\mu }^{-}$, or ${\pi }^{+}{\pi }^{-}$, in the mass ranges $0.1$~GeV/$c^2$~$<m_{A^{\prime }}<3.5$~GeV/$c^2$ and $0.2$~GeV/$c^2$~$<m_{h^{\prime }}<10.5$~GeV/$c^2$. We also investigate three inclusive final-states, $2(e^{+}{e}^{-})X$, $2({\mu }^{+}{\mu }^{-})X$, and $(e^{+}{e}^{-})({\mu }^{+}{\mu }^{-})X$, where $X$ denotes a dark photon candidate detected via missing mass, in the mass ranges $1.1$~GeV/$c^2$~$<m_{A^{\prime }}<3.5$~GeV/$c^2$ and $2.2$~GeV/$c^2$~$<m_{h^{\prime }}<10.5$~GeV/$c^2$. Using the entire $977{\mathrm{fb}}^{-1}$ data set collected by Belle, we observe no significant signal. We obtain individual and combined 90$\%$ confidence level upper limits on the branching fraction times the Born cross section, $\mathcal{B}\times {\sigma }_{\mathrm{Born}}$, on the Born cross section, ${\sigma }_{\mathrm{Born}}$, and on the dark photon coupling to the dark Higgs boson times the kinetic mixing between the Standard Model photon and the dark photon, ${\alpha }_D\times {\epsilon }^2$. These limits improve upon and cover wider mass ranges than previous experiments. The limits from the final-states $3({\pi }^{+}{\pi }^{-})$ and $2(e^{+}{e}^{-})X$ are the first placed by any experiment. For ${\alpha }_D$ equal to 1/137, $m_{h^{\prime }}<$ 8 GeV/$c^2$, and $m_{A^{\prime }}<$ 1 GeV/$c^2$, we exclude values of the mixing parameter, $\epsilon$, above $\sim 8\times 10^{-4}$.

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