Search for lepton flavour violating decays of heavy resonances and quantum black holes to $\mathrm{e}\mu$ pairs in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$

A search is reported for heavy resonances decaying into $\mathrm{e}\mu$ final states using proton-proton collision data recorded by the CMS experiment at the CERN LHC at $\sqrt{s}=13~\mathrm{TeV}$, corresponding to an integrated luminosity of $35.9~\mathrm{fb}^{-1}$. The search focuses on resonance masses above $200$ GeV. With no evidence found for physics beyond the standard model in the mass spectrum of selected $\mathrm{e}\mu$ pairs, upper limits are set at the $95\%$ confidence level on the product of the cross section and branching fraction for signals in models that incorporate lepton-flavour violation in interactions of charged leptons. Resonant $\tau$ sneutrino production in R-parity violating supersymmetry is excluded for $\tau$ sneutrino masses below $1.7$ TeV, and couplings $\lambda_{132}=\lambda_{231}=\lambda'_{311}=0.01$. Heavy Z' gauge bosons in lepton flavour violating transitions are excluded up to $4.4$ TeV. The $\mathrm{e}\mu$ mass spectrum is also interpreted in terms of a non-resonant contribution from quantum black hole production in models with extra spatial dimensions. The exclusion limits range from $3.6$ TeV to $5.6$ TeV for number of extra dimensions between one and six.