A search is reported for heavy resonances and quantum black holes decaying into e$\mu$, e$\tau$, and $\mu\tau$ final states in proton-proton collision data recorded by the CMS experiment at the CERN LHC during 2016-2018 at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The e$\mu$, e$\tau$, and $\mu\tau$ invariant mass spectra are reconstructed, and no evidence is found for physics beyond the standard model. Upper limits are set at 95% confidence level on the product of the cross section and branching fraction for lepton flavor violating signals. Three benchmark signals are studied: resonant $\tau$ sneutrino production in $R$ parity violating supersymmetric models, heavy Z' gauge bosons with lepton flavor violating decays, and nonresonant quantum black hole production in models with extra spatial dimensions. Resonant $\tau$ sneutrinos are excluded for masses up to 4.2 TeV in the e$\mu$ channel, 3.7 TeV in the e$\tau$ channel, and 3.6 TeV in the $\mu\tau$ channel. A Z' boson with lepton flavor violating couplings is excluded up to a mass of 5.0 TeV in the e$\mu$ channel, up to 4.3 TeV in the e$\tau$ channel, and up to 4.1 TeV in the $\mu\tau$ channel. Quantum black holes in the benchmark model are excluded up to the threshold mass of 5.6 TeV in the e$\mu$ channel, 5.2 TeV in the e$\tau$ channel, and 5.0 TeV in the $\mu\tau$ channel. In addition, model-independent limits are extracted to allow comparisons with other models for the same final states and similar event selection requirements. The results of these searches provide the most stringent limits available from collider experiments for heavy particles that undergo lepton flavor violating decays.
Mass distributions for the e$\mu$ channel. In addition to the observed data (black points) and SM prediction (filled histograms), expected signal distributions for three models are shown: the RPV SUSY model with $\lambda = \lambda' = 0.01$ and $\tau$ sneutrino mass of 1.6 TeV, a Z′ boson ($\mathcal{B}=0.1$) with a mass of 1.6 TeV , and the QBH signal expectation for $n=4$ and a threshold mass of 1.6 TeV. The bin width gradually increases with mass.
Mass distributions for the e$\tau$ channel. In addition to the observed data (black points) and SM prediction (filled histograms), expected signal distributions for three models are shown: the RPV SUSY model with $\lambda = \lambda' = 0.01$ and $\tau$ sneutrino mass of 1.6 TeV, a Z′ boson ($\mathcal{B}=0.1$) with a mass of 1.6 TeV , and the QBH signal expectation for $n=4$ and a threshold mass of 1.6 TeV. The bin width gradually increases with mass.
Mass distributions for the $\mu\tau$ channel. In addition to the observed data (black points) and SM prediction (filled histograms), expected signal distributions for three models are shown: the RPV SUSY model with $\lambda = \lambda' = 0.01$ and $\tau$ sneutrino mass of 1.6 TeV, a Z′ boson ($\mathcal{B}=0.1$) with a mass of 1.6 TeV , and the QBH signal expectation for $n=4$ and a threshold mass of 1.6 TeV. The bin width gradually increases with mass.
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