Title: Search for a $μ^+μ^-$ resonance in four-muon final states at Belle II

Abstract: We report on a search for a resonance $X$ decaying to a pair of muons in $e^{+}e^{-}\rightarrow \mu^+ \mu^- X$ events in the 0.212-9.000 GeV/$c^{2}$ mass range, using 178 fb$^{-1}$ of data collected by the BelleII experiment at the SuperKEKB collider at a center of mass energy of 10.58 GeV. The analysis probes two different models of $X$ beyond the standard model: a $Z^{\prime}$ vector boson in the $L_{\mu}-L_{\tau}$ model and a muonphilic scalar. We observe no evidence for a signal and set exclusion limits at the 90\% confidence level on the products of cross section and branching fraction for these processes, ranging from 0.046 fb to 0.97 fb for the $L_{\mu}-L_{\tau}$ model and from 0.055 fb to 1.3 fb for the muonphilic scalar model. For masses below 6 GeV/$c^{2}$, the corresponding constraints on the couplings of these processes to the standard model range from 0.0008 to 0.039 for the $L_{\mu}-L_{\tau}$ model and from 0.0018 to 0.040 for the muonphilic scalar model. These are the first constraints on the muonphilic scalar from a dedicated search.