Improved measurements of $D^0 \to K^-\ell^+\nu_\ell$ and $D^+ \to \bar K^0\ell^+\nu_\ell$

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 $D^0\to K^-e^+\nu_e$, $D^0\to K^-\mu^+\nu_\mu$, $D^+\to \bar K^0e^+\nu_e$, and $D^+\to \bar K^0\mu^+\nu_\mu$ to be $(3.521\pm0.009_{\rm stat.}\pm0.016_{\rm syst.}) \%$, $(3.419\pm0.011_{\rm stat.}\pm0.016_{\rm syst.}) \%$, $(8.864\pm0.039_{\rm stat.}\pm0.082_{\rm syst.}) \%$, and $(8.665\pm0.046_{\rm stat.}\pm0.084_{\rm syst.}) \%$, respectively. By performing a simultaneous fit to the partial decay rates of these four decays, the product of the hadronic form factor $f^K_+(0)$ and the modulus of the $c\to s$ CKM matrix element $|V_{cs}|$ is determined to be $f^K_+(0)|V_{cs}|=0.7171\pm0.0011_{\rm stat.}\pm0.0013_{\rm syst.}$. Taking the value of $|V_{cs}|=0.97349\pm0.00016$ from the standard model global fit or that of $f^K_+(0)=0.7452\pm0.0031$ from the LQCD calculation as input, we derive the results $f^K_+(0)=0.7366\pm0.0011_{\rm stat.}\pm0.0013_{\rm syst.}$ and $|V_{cs}|=0.9623\pm0.0015_{\rm stat.}\pm0.0017_{\rm syst.}\pm0.0040_{\rm LQCD}$.