Improved measurements of ${D}^{0}\to {K}^{-}{\ell }^{+}{\nu }_{\ell }$ and ${D}^{+}\to {\overline{K}}^{0}{\ell }^{+}{\nu }_{\ell }$

Using $7.93\text{}\text{}{\mathrm{fb}}^{-1}$ 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 ${D}^{0}\to {K}^{-}{e}^{+}{\nu }_{e}$, ${D}^{0}\to {K}^{-}{\mu }^{+}{\nu }_{\mu }$, ${D}^{+}\to {\overline{K}}^{0}{e}^{+}{\nu }_{e}$, and ${D}^{+}\to {\overline{K}}^{0}{\mu }^{+}{\nu }_{\mu }$ to be $\left(3.521±0.00{9}_{\mathrm{stat}}±0.01{6}_{\mathrm{syst}}\right)%$, $\left(3.419±0.01{1}_{\mathrm{stat}}±0.01{6}_{\mathrm{syst}}\right)%$, $\left(8.864±0.03{9}_{\mathrm{stat}}±0.08{2}_{\mathrm{syst}}\right)%$, and $\left(8.665±0.04{6}_{\mathrm{stat}}±0.08{4}_{\mathrm{syst}}\right)%$, respectively. By performing a simultaneous fit to the partial decay rates of these four decays, the product of the hadronic form factor ${f}_{+}^{K}\left(0\right)$ and the modulus of the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cs}|$ is determined to be ${f}_{+}^{K}\left(0\right)|{V}_{cs}|=0.7171±0.001{1}_{\mathrm{stat}}±0.001{3}_{\mathrm{syst}}$. Taking the value of $|{V}_{cs}|=0.97349±0.00016$ from the standard model global fit or that of ${f}_{+}^{K}\left(0\right)=0.7452±0.0031$ from the lattice quantum chromodynamics calculation as input, we derive the results ${f}_{+}^{K}\left(0\right)=0.7366±0.001{1}_{\mathrm{stat}}±0.001{3}_{\mathrm{syst}}$. and $|{V}_{cs}|=0.9623±0.001{5}_{\mathrm{stat}}±0.001{7}_{\mathrm{syst}}±0.004{0}_{\mathrm{LQCD}}$.