Measurement of the branching fraction of leptonic decay Ds+ →τ+ντ 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 Ds+→τ+ντ, with τ+→π+π0ν¯τ, to be BDs+→τ+ντ=(5.29±0.25stat±0.20syst)%. We estimate the product of the Cabibbo-Kobayashi-Maskawa matrix element |Vcs| and the Ds+ decay constant fDs+ to be fDs+|Vcs|=(244.8±5.8stat±4.8syst) MeV, using the known values of the τ+ and Ds+ masses as well as the Ds+ lifetime, together with our branching fraction measurement. Combining the value of |Vcs| obtained from a global fit in the standard model and fDs+ from lattice quantum chromodynamics, we obtain fDs+=(251.6±5.9stat±4.9syst) MeV and |Vcs|=0.980±0.023stat±0.019syst. Using the branching fraction of BDs+→μ+νμ=(5.35±0.21)×10-3, we obtain the ratio of the branching fractions BDs+→τ+ντ/BDs+→μ+νμ=9.89±0.71, which is consistent with the standard model prediction of lepton flavor universality.