A search for the charged lepton flavor violating $\tau \rightarrow 3\mu$ decay was performed by the CMS experiment at the LHC, using data collected in 2017-2018 during proton-proton collisions. This data sample corresponds to an integrated luminosity of 97.7 $\mathrm{fb^{-1}}$, recorded at a center-of-mass energy of 13 TeV. Tau leptons produced by the decays of heavy flavor mesons (B and D) or W bosons are exploited in the analysis, with a tailored strategy designed for the two different cases, and combined for the final result.
No significant excess was observed, and an upper limit on the branching fraction $\mathcal{B}(\tau \rightarrow 3\mu)$ of $3.1 \times 10^{-8}$ at 90% confidence level was set. Finally, this result was combined with the earlier CMS search based on 2016 data, resulting in a final observed (expected) upper limit on $\mathcal{B}(\tau \rightarrow 3\mu)$ of $2.9 \times 10^{-8}\ (2.4 \times 10^{-8})$ at 90% confidence level.
To complement this search, a description of the improved version of the trigger designed for this analysis for the next LHC data taking period, started in 2022, is presented.