The search for lepton-flavor violating decays of the Higgs boson to an electron-muon pair using data from proton-proton collisions at $\sqrt{s} = 13$ TeV collected by the CMS experiment at the LHC is presented. The dataset corresponds to an integrated luminosity of $138 fb^{-1}$. No significant excess of events is observed for the 125 GeV Higgs. This analysis leads to the most stringent upper limits at 95\% confidence level so far on the branching fraction of the 125 GeV Higgs boson decaying into an electron and a muon, with an observed (expected) limit of 4.4 (4.7)$\times$10$^{-5}$.
A search for additional scalar resonances, X, in the same decay channel, leads to upper limits on the cross-section of pp$\rightarrow$X$\rightarrow$e$\mu$ in the mass-range of 110-160 GeV. Here, an excess of events is observed at an electron-muon invariant mass of approximately 146 GeV with a local (global) significance of 3.8 (2.8) standard deviations. These results provide valuable insights into lepton-flavor-violating Higgs decays and contribute to our understanding of the Higgs boson sector and potential physics beyond the Standard Model.