The 3.6 σ discrepancy between the predicted and measured value of the anomalous magnetic moment of positive muons can be explained by the existence of a new dark boson Zμ with a mass in sub-GeV range, which is coupled predominantly to the second and third lepton generations through the Lμ − Lτ current. If the Zμ exists, it could be observed in the reaction μ + Z → μ + Z + Zμ of muon scattering off nuclei by looking for an excess of events with the large missing muon beam energy in a detector due to the prompt bremsstrahlung Zμ decays,  Zμ → νν, into a couple of neutrino. The preliminary study of the feasibility for the proposed search shows,  that this specific signal allows the search for the Zμ with the sensitivity in coupling constant αμ >10−11, which is three orders of magnitude higher the value required to explain the discrepancy. The availability of high energy and intensity muon beams at CERN SPS provides unique opportunity either to discover or rule out the Zμ in the proposed search in the near future. The experiment is based on the missing energy approach developed for the searches for invisible decays of dark photons and (pseudo)scalar mesons at CERN and is complementary to these searches.

See, arXiv: 1412.1400; hep-ph/0102222.