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A search is performed for heavy neutrinos in the decay of a $W$ boson intotwo muons and a jet. The data set corresponds to an integrated luminosity ofapproximately $3.0 \text{ fb}^{-1}$ of proton-proton collision data atcentre-of-mass energies of 7 and $8 \text{ TeV}$ collected with the LHCbexperiment. Both same-sign and opposite-sign muons in the final state areconsidered. Data are found to be consistent with the expected background. Upperlimits on the coupling of a heavy neutrino with the Standard Model neutrino areset at $95\%$ confidence level in the heavy-neutrino mass range from 5 to $50\text{ GeV}/c^2$. These are of the order of $10^{-3}$ forlepton-number-conserving decays and of the order of $10^{-4}$ forlepton-number-violating heavy-neutrino decays.

Search for heavy neutral leptons in $W^+\to\mu^{+}\mu^{\pm}\text{jet}$ decays