Search for an invisibly decaying $Z^{prime}$ boson at Belle II in $e^+ e^- to mu^+ mu^- (e^{pm} mu^{mp})$ 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 $e^+ e^- to mu^+ mu^- Z^{prime}$ and of a lepton-flavor-violating $Z^{prime}$ in $e^+ e^- to e^{pm} mu^{mp} Z^{prime}$. 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 $L_{mu}-L_{tau}$ 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/$c^2$.