Search for the Charged-Lepton-Flavor Violating decay $Z\rightarrow e\mu$ in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

A search is presented for the charged-lepton-flavor violating process $Z\rightarrow e\mu$ using 139~fb$^{-1}$ of $pp$ collision data collected with the ATLAS experiment at $\sqrt{s}=13$ TeV. An excess in the $e\mu$ invariant mass spectrum near the $Z$ boson mass would be a striking signature of new physics. No excess is observed, and an upper limit is placed on the branching fraction ${\cal B}(Z\rightarrow e\mu) < 3.04 \times 10^{-7}$ at 95\% confidence level, calculated via a ratio to the average of observed yields of $ee$ and $\mu\mu$ events to significantly reduce systematic uncertainties.