Muon g-2 and searches for a new leptophobic sub-GeV dark boson in a missing-energy experiment at CERN

The 3.6 sigma discrepancy between the predicted and measured values of the anomalous magnetic moment of positive muons can be explained by the existence of a new dark boson Z(mu) with a mass in the sub- GeV range, which is coupled predominantly to the second and third lepton generations through the L-mu - L-tau current. After a discussion of the present phenomenological bounds on the Z(mu) coupling, we show that if the Z(mu) exists, it could be observed in the reaction mu + Z -> mu + Z + Z(mu) of a muon scattering off nuclei by looking for an excess of events with large missing muon beam energy in a detector due to the prompt bremsstrahlung Z(mu) decay Z(mu) -> nu nu into a couple of neutrinos. We describe the experimental technique and the preliminary study of the feasibility for the proposed search. We show that this specific signal allows for a search for the Z(mu) with a sensitivity in the coupling constant alpha(mu) greater than or similar to 10(-11), which is 3 orders of magnitude higher than the value required to explain the discrepancy. We point out that the availability of high- energy and - intensity muon beams at CERN SPS provides a unique opportunity to either discover or rule out the Z(mu) 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 experiments.