The L & mu; - L & tau; extension of the standard model predicts the existence of a lepton-flavor-universality -violating Z0 boson that couples only to the heavier lepton families. We search for such a Z0 through its invisible decay in the process e thorn e- & RARR; & mu; thorn & mu;-Z0. 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 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 x 10-3 at low Z0 masses to 1 at Z0 masses of 8 GeV/c2.
