Sensitivity study of the charged lepton flavor violating process $\tau \to \gamma \mu$ at STCF

A sensitivity study for the searching of the charged lepton flavor violating process $\tau \to \gamma\mu$ at the Super $\tau$-Charm Facility is performed with a fast simulation. With the expected performance of current detector design and the integrated luminosity of $1\text{ab}^{-1}$ in one year, the sensitivity on the branching fraction (BF) of $\tau \to \gamma\mu$ is estimated to be at the level of $10^{-8}$. The sensitivity under different detector performances are also studied. With ideal performance, the BF could be probed to be $1.8 \times 10^{-8}$ at 90% confidence level. The sensitivity is expected to scale with the square root of the luminosity, therefore with a total luminosity of $10\text{ab}^{-1}$ corresponding to ten-year of data taking, the sensitivity could reach $5.7 \times 10^{-9}$, which is about one order of magnitude improvement upon the current best upper limit.