We discuss the feasibility of detecting the gauge boson of the $U(1{)}_{L_{\mu }-L_{\tau }}$ 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 $Z^{\prime }$ 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 $e^{+}{e}^{-}\to \gamma Z^{\prime }\to \gamma \nu \overline{\nu }$ (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 $Z^{\prime }$, 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 $Z^{\prime }$ with the mass $M_{Z^{\prime }}\lesssim 1\mathrm{GeV}$ and the new gauge coupling $g_{Z^{\prime }}\gtrsim 8\times {10}^{-4}$, 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.

• Received 6 February 2017

DOI:https://doi.org/10.1103/PhysRevD.95.055006