Searching for $\tau \rightarrow \mu \gamma$ lepton-flavor-violating decay at super charm-tau factory

We investigate the possibility of searching the lepton-flavor-violating (LFV) $\tau\rightarrow \mu\gamma$ rare decay at the Super Charm-Tau Factory (CTF). By comparing the kinematic distributions of the LFV signal and the standard model (SM) background, we develop an optimized event selection criteria which can significantly reduce the background events. It is concluded that new $2 \sigma$ upper limit of about $1.9 \times 10^{-9}$ on $Br(\tau \rightarrow \mu \gamma)$ can be obtained at the CTF, which is beyond the capability of Super-B factory in searching $\tau$ lepton rare decay. Within the framework of the scalar leptoquark model, a joint constraint on $\lambda_1 \lambda_2$ and $M_{LQ}$ can be derived from the upper bound on $Br(\tau \rightarrow \mu \gamma)$. With $1000~ fb^{-1}$ data expected at the CTF, we get $\lambda_1\lambda_2 < 7.2 \times 10^{-2}~(M_{LQ} = 800~ {\rm GeV})$ and $M_{LQ} > 900~{\rm GeV}~(\lambda_1 \lambda_2 = 9 \times 10^{-2})$ at $95\%$ confidence level (C.L.).