Search for an invisible $Z^{\mathrm{\prime }}$ in a final state with two muons and missing energy at Belle II

The $L_{\mu }-L_{\tau }$ extension of the standard model predicts the existence of a lepton-flavor-universality-violating $Z^{\mathrm{\prime }}$ boson that couples only to the heavier lepton families. We search for such a $Z^{\mathrm{\prime }}$ through its invisible decay in the process $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}{Z}^{\mathrm{\prime }}$. We use a sample of electron-positron collisions at a center-of-mass energy of 10.58GeV collected by the Belle II experiment in 2019-2020, corresponding to an integrated luminosity of 79.7fb${}^{-1}$. We find no excess over the expected standard-model background. We set 90$\mathrm{\%}$-confidence-level upper limits on the cross section for this process as well as on the coupling of the model, which ranges from $3\times {10}^{-3}$ at low $Z^{\mathrm{\prime }}$ masses to 1 at $Z^{\mathrm{\prime }}$ masses of 8$GeV\mathrm{/}{c}^2$.