Determination of f₊^K(0) and extraction of |V_cs| from semileptonic D decays

By globally analyzing all existing measured branching fractions and partial rates in different four momentum transfer-squared q² bins of D→Ke⁺ν_e decays, we obtain the product of the form factor and magnitude of Cabibbo–Kobayashi–Maskawa matrix element V_cs to be f₊^K(0)|V_cs|=0.717±0.004. With this product, we determine the D→K semileptonic form factor f₊^K(0)=0.737±0.004±0.000 in conjunction with the value of |V_cs| determined from the standard model global fit. Alternately, with the product together with the input of the form factor f₊^K(0) calculated in lattice quantum chromodynamics (LQCD) recently, we extract |V_cs|^D→Ke+ν_e=0.962±0.005±0.014, where the error is still dominated by the uncertainty of the form factor calculated in LQCD. Combining the |V_cs|^{D_s+→ℓ+ν_ℓ}=1.012±0.015±0.009 extracted from all existing measurements of D_s⁺→ℓ⁺ν_ℓ decays and |V_cs|^D→Ke+ν_e=0.962±0.005±0.014 together, we find the most precisely determined |V_cs| to be |V_cs|=0.983±0.011, which improves the accuracy of the PDG'2014 value |V_cs|^PDG′2014=0.986±0.016 by 45 %