| Summary: | Abstract We report a sensitive study of $$D_s^+ \rightarrow \tau ^+ \nu _{\tau }$$ D s + → τ + ν τ decay via $$\tau ^+ \rightarrow e^+ \nu _e \bar{\nu }_{\tau }$$ τ + → e + ν e ν ¯ τ with an integrated luminosity of 1 ab $$^{-1}$$ - 1 at the center-of-mass energy of 4.009 GeV at a future Super Tau Charm Facility (STCF). Under the help of the fast simulation software package, the statistical sensitivity for the absolute branching fraction of $$D_s^+ \rightarrow \tau ^+ \nu _{\tau }$$ D s + → τ + ν τ is determined to be $$2\times 10^{-4}$$ 2 × 10 - 4 . Combining with our previous prospect of $$D_s^+ \rightarrow \mu ^+ \nu _{\mu }$$ D s + → μ + ν μ , the ratio of the branching fractions for $$D_s^+ \rightarrow \tau ^+ \nu _{\tau }$$ D s + → τ + ν τ over $$D_s^+ \rightarrow \mu ^+ \nu _{\mu }$$ D s + → μ + ν μ can achieve a relative statistical precision of 0.5%, which will provide the most stringent test of the $$\tau $$ τ - $$\mu $$ μ lepton flavor universality in heavy quark decays. Taking the decay constant $$f_{D_s^+}$$ f D s + from lattice QCD calculations or the CKM matrix element $$|V_{cs}|$$ | V cs | from the CKMfitter group as an input, the relative statistical uncertainties for $$|V_{cs}|$$ | V cs | and $$f_{D_s^+}$$ f D s + are estimated to be 0.3% and 0.2%, respectively.
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