A search is presented for massive long-lived particles decaying into a muon and two quarks. The dataset consists of proton-proton interactions at centre-of-mass energies of 7 and 8 TeV, corresponding to integrated luminosities of 1 and 2 $$\,\hbox {fb}^{-1}$$ , respectively. The analysis is performed assuming a set of production mechanisms with simple topologies, including the production of a Higgs-like particle decaying into two long-lived particles. The mass range from 20 to 80 $$\mathrm{{GeV}}/c^2$$ and lifetimes from 5 to 100 $${\,\mathrm{{ps}}}$$ are explored. Results are also interpreted in terms of neutralino production in different R-Parity violating supersymmetric models, with masses in the 23–198 GeV/ $$c^2$$ range. No excess above the background expectation is observed and upper limits are set on the production cross-section for various points in the parameter space of theoretical models.