Detecting the $L_{\mu }-L_{\tau }$ gauge boson at Belle II

Abstract

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 $e^{+}{e}^{-}\to \gamma Z^{\prime }\to \gamma \nu \bar{\nu }(missingenergy)$ 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 $M_{Z^{\prime }}\lesssim 1$ GeV and the new gauge coupling $g_{Z^{\prime }}\gtrsim 8\cdot 10^{-4}$, 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.

10 pages, 10 figures: v2; title changed, references added, FIG. 4,5,7, and 8 changed, Footnotes added, conclusion unchanged

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