Long-lived particles decaying to e±μ∓ν, with masses between 7 and 50GeV/c2 and lifetimes between 2 and 50ps, are searched for by looking at displaced vertices containing electrons and muons of opposite charges. The search is performed using 5.4fb−1 of p p collisions collected with the LHCb detector at a centre-of-mass energy of s√=13TeV. Three mechanisms of production of long-lived particles are considered: the direct pair production from quark interactions, the pair production from the decay of a Standard-Model-like Higgs boson with a mass of 125GeV/c2, and the charged current production from an on-shell W boson with an additional lepton. No evidence of these long-lived states is obtained and upper limits on the production cross-section times branching fraction are set on the different production modes.