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Search for an invisibly decaying $Z^{\prime}$ boson at Belle II in $e^+ e^- \to μ^+ μ^- (e^{\pm} μ^{\mp})$ plus missing energy final states

Theories beyond the standard model often predict the existence of an additional neutral boson, the $Z^{\prime}$. Using data collected by the Belle II experiment during 2018 at the SuperKEKB collider, we perform the first searches for the invisible decay of a $Z^{\prime}$ in the process $e^+ e^- \to μ^+ μ^- Z^{\prime}$ and of a lepton-flavor-violating $Z^{\prime}$ in $e^+ e^- \to e^{\pm} μ^{\mp} Z^{\prime}$. We do not find any excess of events and set 90\% credibility level upper limits on the cross sections of these processes. We translate the former, in the framework of an $L_μ-L_τ$ theory, into upper limits on the $Z^{\prime}$ coupling constant at the level of $5 \times 10^{-2}$ -- $1$ $M_{Z^\prime}\leq 6$ GeV/$c^2$.