Searching for $τ\rightarrow μγ$ lepton-flavor-violating decay at super charm-tau factory

We investigate the possibility of searching the lepton-flavor-violating (LFV) $τ\rightarrow μγ$ 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 $2 σ$ upper limit of about $1.9 \times 10^{-9}$ on $Br(τ\rightarrow μγ)$ can be obtained at the CTF, which is beyond the capability of Super-B factory in searching $τ$ lepton rare decay. Within the framework of the scalar leptoquark model, a joint constraint on $λ_1 λ_2$ and $M_{LQ}$ can be derived from the upper bound on $Br(τ\rightarrow μγ)$. With $1000~ fb^{-1}$ data expected at the CTF, we get $λ_1λ_2 < 7.2 \times 10^{-2}~(M_{LQ} = 800~ {\rm GeV})$ and $M_{LQ} > 900~{\rm GeV}~(λ_1 λ_2 = 9 \times 10^{-2})$ at $95\%$ confidence level (C.L.).

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