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We report a feasibility study of pure leptonic decay $D_s^+\to\mu^+\nu_\mu$by using a fast simulation software package at STCF. With an expectedluminosity of $1~\mathrm{ab}^{-1}$ collected at STCF at a center-of-mass energyof 4.009 GeV, the statistical sensitivity of the branching fraction isdetermined to be 0.3\%. Combining this result with the $c\rightarrow s$ quarkmixing matrix element $|V_{cs}|$ determined from the current global StandardModel fit, the statistical sensitivity of $D_s^+$ decay constant, $f_{D_s^+}$,is estimated to be 0.2\%. Alternatively, combining the current results of$f_{D_s^+}$ calculated by lattice QCD, the statistical sensitivity of$|V_{cs}|$ is determined to be 0.2\%, which helps probe possible new physicsbeyond. The unprecedented precision to be achieved at STCF will provide aprecise calibration of QCD and rigorous test of Standard Model.

Prospects of CKM elements $|V_{cs}|$ and decay constant $f_{D_{s}^+}$ in $D_s^+\to\mu^+\nu_\mu$ decay at STCF