Detecting the L μ − L τ gauge boson at Belle II

We discuss the feasibility of detecting the gauge boson of the U(1)Lμ−Lτ symmetry, which possesses a mass in the range between MeV and GeV, at the Belle-II experiment. The kinetic mixing between the new gauge boson Z′ and photon is forbidden at the tree level and is radiatively induced. The leptonic force mediated by such a light boson is motivated by the discrepancy in muon anomalous magnetic moment and also the gap in the energy spectrum of cosmic neutrino. Defining the process e+e−→γZ′→γνν¯ (missing energy) to be the signal, we estimate the numbers of the signal and the background events and show the parameter region to which the Belle-II experiment will be sensitive. The signal process in the Lμ−Lτ model is enhanced with a light Z′, which is a characteristic feature differing from the dark photon models with a constant kinetic mixing. We find that the Belle-II experiment with the design luminosity will be sensitive to the Z′ with the mass MZ′≲1 GeV and the new gauge coupling gZ′≳8×10−4, which covers a half of the unconstrained parameter region that explains the discrepancy in muon anomalous magnetic moment. The possibilities to improve the significance of the detection are also discussed.