Measurement of the branching fraction of leptonic decay D⁺_s → τ⁺ν_τ via τ⁺ → π⁺π⁰¯ν_τ

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 BD+s→τ+ντ=(5.29±0.25stat±0.20syst)%. We estimate the product of the Cabibbo-Kobayashi-Maskawa matrix element |Vcs| and the D+s decay constant fD+s to be fD+s|Vcs|=(244.8±5.8stat±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 fD+s from lattice quantum chromodynamics, we obtain fD+s=(251.6±5.9stat±4.9syst)  MeV and |Vcs|=0.980±0.023stat±0.019syst. Using the branching fraction of BD+s→μ+νμ=(5.35±0.21)×10−3, we obtain the ratio of the branching fractions BD+s→τ+ντ/BD+s→μ+νμ=9.89±0.71, which is consistent with the standard model prediction of lepton flavor universality.