Detecting the Lμ- Lτ gauge boson at Belle II

We discuss the feasibility of detecting the gauge boson of the U(l)(L mu-L tau) symmetry, which possesses a mass in the range between MeVand 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(-) -> gamma Z '->gamma nu nu ( 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 L-mu- L-tau model is enhanced with a light Z0, 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 'less than or similar to 1 GeV and the new gauge coupling g(Z ') greater than or similar to 8 x 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.