Search for the Dark Photon and the Dark Higgs Boson at Belle

Abstract

The dark photon ${A}^{\ensuremath{'}}$ and the dark Higgs boson ${h}^{\ensuremath{'}}$ 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 Higgstrahlung channel ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{A}^{\ensuremath{'}}{h}^{\ensuremath{'}}$, with ${h}^{\ensuremath{'}}\ensuremath{\rightarrow}{A}^{\ensuremath{'}}{A}^{\ensuremath{'}}$. We investigate ten exclusive final states with ${A}^{\ensuremath{'}}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$, ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, or ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ in the mass ranges $0.1\text{ }\text{ }\mathrm{GeV}/{c}^{2}\text{ }<{m}_{{A}^{\ensuremath{'}}}<\phantom{\rule{0ex}{0ex}}3.5\text{ }\text{ }\mathrm{GeV}/{c}^{2}$ and $0.2\text{ }\text{ }\mathrm{GeV}/{c}^{2}\text{ }<{m}_{{h}^{\ensuremath{'}}}<10.5\text{ }\text{ }\mathrm{GeV}/{c}^{2}$. We also investigate three inclusive final states $2({e}^{+}{e}^{\ensuremath{-}})X$, $2({\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})X$, and $({e}^{+}{e}^{\ensuremath{-}})({\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})X$, where $X$ denotes a dark photon candidate detected via missing mass, in the mass ranges $1.1\text{ }\text{ }\mathrm{GeV}/{c}^{2}\text{ }<{m}_{{A}^{\ensuremath{'}}}<3.5\text{ }\text{ }\mathrm{GeV}/{c}^{2}$ and $2.2\text{ }\text{ }\mathrm{GeV}/{c}^{2}\text{ }<{m}_{{h}^{\ensuremath{'}}}<10.5\text{ }\text{ }\mathrm{GeV}/{c}^{2}$. Using the entire $977\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ data set collected by Belle, we observe no significant signal. We obtain individual and combined 90% credibility level upper limits on the branching fraction times the Born cross section, $\mathcal{B}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\sigma}}_{\text{Born}}$, on the Born cross section ${\ensuremath{\sigma}}_{\text{Born}}$, and on the dark photon coupling to the dark Higgs boson times the kinetic mixing between the standard model photon and the dark photon, ${\ensuremath{\alpha}}_{D}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\epsilon}}^{2}$. These limits improve upon and cover wider mass ranges than previous experiments. The limits from the final states $3({\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})$ and $2({e}^{+}{e}^{\ensuremath{-}})X$ are the first placed by any experiment. For ${\ensuremath{\alpha}}_{D}$ equal to $1/137$, ${m}_{{h}^{\ensuremath{'}}}<\text{ }8\text{ }\text{ }\mathrm{GeV}/{c}^{2}$, and ${m}_{{A}^{\ensuremath{'}}}<1\text{ }\text{ }\mathrm{GeV}/{c}^{2}$, we exclude values of the mixing parameter $\ensuremath{\epsilon}$ above $\ensuremath{\sim}8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$.