Search for a dark photon and an invisible dark Higgs boson in \(\mu^+\mu^-\) and missing energy final states with the Belle II experiment

The dark photon \(A^\prime\) and the dark Higgs boson \(h^\prime\) are hypothetical particles predicted in many dark sector models. We search for the simultaneous production of \(A^\prime\) and \(h^\prime\) in the dark Higgsstrahlung process \(e^{+}e^{-}\rightarrow A^\prime \, h^\prime\) with \(A^\prime \rightarrow \mu^+\mu^-\) and \( h^\prime\) invisible in electron-positron collisions at a center-of-mass energy of 10.58 GeV collected by the Belle II experiment in 2019. With an integrated luminosity of 8.34 fb\(^{-1}\), we observe no evidence for signal. We obtain exclusion limits at 90% Bayesian credibility in the range of 1.7--5.0 fb on the cross section and in the range of \(1.7 \times10^{-8}\)--\(200 \times10^{-8}\) on the effective coupling \(\varepsilon^2 \times \alpha_D\) for the \(A^\prime\) mass in the range of 4.0 GeV/\(c^2\) \(< M_{A^\prime}< 9.7\) GeV/\(c^2\) and for the \(h^\prime\) mass \(M_{h^\prime} < M_{A^\prime}\), where \(\varepsilon\) is the mixing strength between the standard model and the dark photon and \(\alpha_D\) is the coupling of the dark photon to the dark Higgs boson. Our limits are the first in this mass range.