  The charged lepton flavor violation process is a clean and sensitive probe of
new physics beyond the Standard Model. A sensitivity study is performed to the
process $\tau^- \to \gamma \mu^-$ based on a 3~fb$^{-1}$ inclusive Monte Carlo
sample of $e^+e^-$ collisions at a center-of-mass energy of 4.26 or 4.6~GeV, in
the framework of the BESIII software system. The 90\% confidence level upper
limits on $\BR(\tau^- \to \gamma \mu^-)$ are estimated assuming no signal is
produced. We also obtain the sensitivity on $\BR(\tau^- \to \gamma \mu^-)$ as a
function of the integrated luminosity, to serve as a reference for the HIEPA
being proposed in China. It is found that 6.34~ab$^{-1}$ are needed to reach
the current best upper limit of $4.4\times 10^{-8}$ and about 2510~ab$^{-1}$
are needed to reach a sensitivity of $10^{-9}$ if the detector design is
similar to that of BESIII.
