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

The 3.6 σdiscrepancy 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_μwith a mass in the sub-GeV range, which is coupled predominantly to the second and third lepton generations through the L_μ- L_τcurrent . After a discussion of the present phenomenological bounds on the Z_μcoupling, we show that if the Z_μexists, it could be observed in the reaction μ+Z \to μ+Z+Z_μof 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_μdecay Z_μ\to ννinto 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 the search for the Z_μwith a sensitivity in the coupling constant α_μ> 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_μin 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.