Search for heavy neutral leptons in $$W^+\rightarrow \mu ^{+}\mu ^{\pm }\, \text {jet}$$ W + → μ + μ ± jet decays

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