Search for the Lepton-Flavor Violating Decay of the Higgs Boson and Additional Higgs Bosons in the Electron-Muon Final State

This dissertation presents a search for the lepton-flavor violating decay of the Higgs boson and potential additional Higgs bosons with a mass of 110-160 GeV to a pair of oppositely-charged electron-muon. A proton-proton collision data set at a center-of-mass energy of 13 TeV and an integrated luminosity of 138 fb^-1 collected by the Compact Muon Solenoid experiment at the Large Hadron Collider is used. No excess is observed for the Higgs boson. The observed (expected) upper limit on the branching fraction is determined to be 4.4 (4.7) x 10^-5 at 95% confidence level, the most stringent direct limit thus far. For the additional Higgs boson, the largest excess of events over the expected background is observed at an electron-muon invariant mass of around 146 GeV. The local (global) significance of the excess is 3.8 (2.8) standard deviations in the full mass range of the search. This is the first direct search for additional Higgs bosons with a mass of 110-160 GeV in the electron-muon final state.