Search for heavy resonances and quantum black holes in e$\mu$, e$\tau$, and $\mu\tau$ final states in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$

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 collisions recorded by the CMS experiment at the CERN LHC at $\sqrt{s}=13~\mathrm{TeV}$, corresponding to an integrated luminosity of $137.1~\mathrm{fb}^{-1}$. No evidence is found for physics beyond the standard model in the dilepton invariant mass spectra, and upper limits are set at $95\%$ confidence level on the products of the cross sections and branching fractions for various lepton-flavor violating signals. These include resonant $\tau$ sneutrino production in R-parity violating supersymmetric models, heavy $Z'$ gauge bosons with lepton-flavor violating transitions, and non-resonant quantum black-hole production in models with extra spatial dimensions. In addition, model-independent limits are provided allowing the results to be interpreted in other models with the same final states and similar kinematic distributions. The results of these searches provide the best collider limits to date for the models considered.