Improved measurements of D⁰ → K⁻l⁺ ν_l and D⁺ → K¯⁰l⁺ ν_l

Using 7.93 fb−1 of eþe− 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−eþνe, D0 → K−μþνμ, Dþ →K¯ 0eþνe, and Dþ →K¯ 0μþνμ to be ð3.5210.009stat0.016systÞ%, ð3.4190.011stat0.016systÞ%, ð8.864 0.039stat 0.082systÞ%, and ð8.665 0.046stat 0.084systÞ%, respectively. By performing a
simultaneous fit to the partial decay rates of these four decays, the product of the hadronic form factor fK þð0Þ and the modulus of the c → s Cabibbo-Kobayashi-Maskawa matrix element jVcsj is determined to be fK
þð0ÞjVcsj ¼ 0.7171 0.0011stat 0.0013syst. Taking the value of jVcsj ¼ 0.97349 0.00016 from the standard model global fit or that of fK þð0Þ ¼ 0.7452 0.0031 from the lattice quantum chromodynamics calculation as input, we derive the results fK þð0Þ ¼ 0.7366 0.0011stat 0.0013syst. and jVcsj ¼ 0.9623 0.0015stat 0.0017syst 0.0040LQCD.