| Summary: | Abstract We report a feasibility study of pure leptonic decay $$D_s^+\rightarrow \mu ^+\nu _\mu $$ D s + → μ + ν μ by using a fast simulation software package at STCF. With an expected luminosity of $$1~\mathrm {ab}^{-1}$$ 1 ab - 1 collected at STCF at a center-of-mass energy of 4.009 GeV, the statistical sensitivity of the branching fraction is determined to be 0.3%. Combining this result with the $$c \rightarrow s$$ c → s quark mixing matrix element $$|V_{cs}|$$ | V cs | determined from the current global Standard Model fit, the statistical sensitivity of $$D_s^+$$ D s + decay constant, $$f_{D_s^+}$$ f D s + , is estimated to be 0.2%. Alternatively, combining the current results of $$f_{D_s^+}$$ f D s + calculated by lattice QCD, the statistical sensitivity of $$|V_{cs}|$$ | V cs | is determined to be 0.2%, which helps probe possible new physics beyond Standard Model. The unprecedented precision to be achieved at STCF will provide a precise calibration of QCD and rigorous test of Standard Model.
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