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By analyzing 6.32 fb − 1 of e+ e− annihilation data collected at the center-of-mass energies between 4.178 and 4.226 GeV with the BESIII detector, we determine the branching fraction of the leptonic decay D + s → τ + ντ, with τ+ → π + π0¯ντ, to be B D + s → τ + ν τ = (5.29 ± 0.25 stat ± 0.20 syst) %. We estimate the product of the Cabibbo-Kobayashi-Maskawa matrix element |Vcs|and the D + s decay constant f D + s to be f D + s|Vcs| = (244.8 ± 5.8 stat ± 4.8syst) MeV, using the known values of the τ + and D + s masses as well as the D + s lifetime, together with our branching fraction measurement. Combining the value of |Vcs| obtained from a global fit in the standard model and f D + s from lattice quantum chromodynamics, we obtain f D + s = (251.6 ± 5.9 stat ± 4.9syst) MeV and |Vcs| = 0.980 ± 0.023 stat ± 0.019 syst. Using the branching fraction of B D + s → μ + νμ = (5.35±0.21)×10−3, we obtain the ratio of the branching fractions B D + s → τ + ντ/B D +s → μ+νμ = 9.89±0.71, which is consistent with the standard model prediction of lepton flavor universality.
By using 6.32 fb−1 of data collected with the BESIII detector at center-of-mass energies between 4.178 and 4.226 GeV, we perform an amplitude analysis of the decay D+s ! K0S + 0 and determine the relative fractions and phase differences of different intermediate processes, which include K0S (770)+, K0S (1450)+, K (892)0 +, K (892)+ 0, and K (1410)0 +. With the detection efficiency based on the amplitude analysis results, the absolute branching fraction is measured to be B(D+s ! K0S + 0) = (5.43 ± 0.30stat ± 0.15syst) × 10−3.