Search for the lepton-flavour violating decay $D^0\to e^{\pm }{\mu }^{\mp }$

A search for the lepton-flavour violating decay $D^0\to e^{\pm }{\mu }^{\mp }$ is made with a dataset corresponding to an integrated luminosity of 3.0 fb${}^{-1}$ of proton-proton collisions at centre-of-mass energies of $7$ TeV and $8$ TeV, collected by the LHCb experiment. Candidate $D^0$ mesons are selected using the decay $D^{\ast +}\to D^0{\pi }^{+}$ and the $D^0\to e^{\pm }{\mu }^{\mp }$ branching fraction is measured using the decay mode $D^0\to K^{-}{\pi }^{+}$ as a normalisation channel. No significant excess of $D^0\to e^{\pm }{\mu }^{\mp }$ candidates over the expected background is seen, and a limit is set on the branching fraction, $\mathcal{B}(D^0\to e^{\pm }{\mu }^{\mp })<1.3\times {10}^{-8}$, at 90 % confidence level. This is an order of magnitude lower than the previous limit and it further constrains the parameter space in some leptoquark models and in supersymmetric models with R-parity violation.