Sensitivity study of the charged lepton flavor violating process $$\tau \rightarrow \gamma \mu $$ τ → γ μ at STCF

A sensitivity study for the search for the charged lepton flavor violating process $$\tau \rightarrow \gamma \mu $$ τ → γ μ at the Super $$\tau $$ τ -Charm Facility is performed with a fast simulation. With the expected performance of the current detector design and an integrated luminosity of $$1\,\textrm{ab}^{-1}$$ 1 ab - 1 corresponding to one-year of data taking, the sensitivity on the branching fraction (BF) of $$\tau \rightarrow \gamma \mu $$ τ → γ μ is estimated to be at the level of $$10^{-8}$$ 10 - 8 . The sensitivity under different detector performances are also studied. With ideal performance, the BF could be probed to be $$2.8\,\times \,10^{-8}$$ 2.8 × 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 $$10\,\hbox {ab}^{-1}$$ 10 ab - 1 corresponding to ten-year of data taking, the sensitivity could reach $$8.8\,\times 10^{-9}$$ 8.8 × 10 - 9 , which is about one order of magnitude improvement upon the current best upper limit.