Sensitivity study of the charged lepton flavor violating process $τ\to γμ$ at STCF
A sensitivity study for the search for the charged lepton flavor violating process $τ\to γμ$ at the Super $τ$-Charm Facility is performed with a fast simulation. With the expected performance of the current detector design and an integrated luminosity of \SI{1}{ab^{-1}} corresponding to one-year of data taking, the sensitivity on the branching fraction (BF) of $τ\to γμ$ is estimated to be at the level of \num{e-8}. The sensitivity under different detector performances are also studied. With ideal performance, the BF could be probed to be \num{2.8e-8} at \SI{90}{\percent} confidence level. The sensitivity is expected to scale with the square root of the luminosity, therefore with a total luminosity of \SI{10}{ab^{-1}} corresponding to ten-year of data taking, the sensitivity could reach \num{8.8e-9}, which is about one order of magnitude improvement upon the current best upper limit.