Improved measurements of D⁰ → K⁻⁺ν_ and $D^+ → K^0^+ν_$

Using 7.93 fb⁻¹ of e⁺e⁻ collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we measure the absolute branching fractions of D⁰→ K⁻e⁺νₑ, D⁰→ K⁻μ⁺ν_μ, D⁺→ K⁰e⁺νₑ, and D⁺→ K⁰μ⁺ν_μ to be (3.509±0.009stat.±0.013syst.) %, (3.408±0.011stat.±0.013syst.) %, (8.856±0.039stat.±0.078syst.) %, and (8.661±0.046stat.±0.080syst.) %, respectively. By performing a simultaneous fit to the partial decay rates of these four decays, the product of the hadronic form factor fK₊(0) and the modulus of the c→ s CKM matrix element |Vcs| is determined to be fK₊(0)|Vcs|=0.7162±0.0011stat.±0.0012syst.. Taking the value of |Vcs|=0.97349±0.00016 from the standard model global fit or that of fK₊(0)=0.7452±0.0031 from the LQCD calculation as input, we derive the results fK₊(0)=0.7357±0.0011stat.±0.0012syst. and |Vcs|=0.9611±0.0015stat.±0.0016syst.±0.0040LQCD.