Lμ-Lτ gauge-boson production from lepton flavor violating τ decays at Belle II

Lμ-Lτ gauge boson (Z′) with a mass in the MeV to GeV region can resolve not only the muon g-2 excess, but also the gap in the high-energy cosmic neutrino spectrum at IceCube. It was recently proposed that such a light gauge boson can be detected during the Belle II experiment with a luminosity of 50 ab-1 by the e+e-→γ+E process through the kinetic mixing with the photon, where the missing energy E is from the Z′→νν decays. We study the phenomenological implications when a pair of singlet vectorlike leptons carrying different Lμ-Lτ charges are included, and a complex singlet scalar (φS) is introduced to accomplish the spontaneous U(1)Lμ-Lτ symmetry breaking. It is found that the extension leads to several phenomena of interest, including (i) branching ratio (BR) for h→μτ can be of the order of 10-3; (ii) φS-mediated muon g-2 can be of the order of 10×10-10; (iii) BR for τ→μφS∗→μZ′Z′ can be 10-8, and (iv) kinetic mixing between the Z′ boson and photon is sensitive to the relative heavy lepton masses. The predicted BRs for τ→(3μ+E,5μ) through the leptonic Z′ decays can reach a level of 10-9, in which the results fall within the sensitivity of the Belle II in the search for the rare tau decays.