Search for $Z^{'} \rightarrow \mu^{+} \mu^{-}$ in the $L_\mu {-} L_\tau$ gauge-symmetric model at Belle

We search for a new gauge boson $Z'$ that couples only to heavy leptons and their corresponding neutrinos in the process $e^{+} e^{-} \rightarrow Z'(\rightarrow \mu^{+}\mu^{-}) \mu^{+}\mu^{-}$, using a 643 fb$^{-1}$ data sample collected by the Belle experiment at or near the $\Upsilon(1S,2S,3S,4S,5S)$ resonances at the KEKB collider. For the first time, effects due to initial state radiation are used in estimating the detection efficiency. No signal is observed in the mass range of 0.212 -- 10 GeV/${\it c}^2$ and we set an upper limit on the coupling strengh, $g'$, constraining $Z'$ as a possible contributor to the anomalous magnetic dipole moment of muon.