Abstract
We report a sensitive study of D_s^+ rightarrow tau ^+ nu _{tau } decay via tau ^+ rightarrow e^+ nu _e bar{nu }_{tau } with an integrated luminosity of 1 ab^{-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 } is determined to be 2times 10^{-4}. Combining with our previous prospect of D_s^+ rightarrow mu ^+ nu _{mu }, the ratio of the branching fractions for D_s^+ rightarrow tau ^+ nu _{tau } over D_s^+ rightarrow mu ^+ nu _{mu } can achieve a relative statistical precision of 0.5%, which will provide the most stringent test of the tau -mu lepton flavor universality in heavy quark decays. Taking the decay constant f_{D_s^+} from lattice QCD calculations or the CKM matrix element |V_{cs}| from the CKMfitter group as an input, the relative statistical uncertainties for |V_{cs}| and f_{D_s^+} are estimated to be 0.3% and 0.2%, respectively.
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