Measurement of the absolute branching fractions for purely leptonic D⁺_s decays

We report new measurements of the branching fraction B(D+s→ℓ+ν), where ℓ+ is either μ+ or τ+(→π+¯ντ), based on 6.32  fb−1 of electron-positron annihilation data collected by the BESIII experiment at six center-of-mass energy points between 4.178 and 4.226 GeV. Simultaneously floating the D+s→μ+νμ and D+s→τ+ντ components yields B(D+s→τ+ντ)=(5.21±0.25±0.17)×10−2, B(D+s→μ+νμ)=(5.35±0.13±0.16)×10−3, and the ratio of decay widths R=Γ(D+s→τ+ντ)Γ(D+s→μ+νμ)=9.73+0.61−0.58±0.36, where the first uncertainties are statistical and the second systematic. No evidence of CP asymmetry is observed in the decay rates D±s→μ±νμ and D±s→τ±ντ: ACP(μ±ν)=(−1.2±2.5±1.0)% and ACP(τ±ν)=(+2.9±4.8±1.0)%. Constraining our measurement to the Standard Model expectation of lepton universality (R=9.75), we find the more precise results B(D+s→τ+ντ)=(5.22±0.10±0.14)×10−2 and ACP(τ±ντ)=(−0.1±1.9±1.0)%. Combining our results with inputs external to our analysis, we determine the c→¯s quark mixing matrix element, D+s decay constant, and ratio of the decay constants to be |Vcs|=0.973±0.009±0.014, fD+s=249.9±2.4±3.5  MeV, and fD+s/fD+=1.232±0.035, respectively.