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

• Received 7 December 2022
• Accepted 19 April 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.231801

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Published by the American Physical Society