Improved measurements ofDmeson semileptonic decays toπandKmesons

Using the entire CLEO-c $\psi (3770)\to D\overline{D}$ event sample, corresponding to an integrated luminosity of $818{\mathrm{pb}}^{-1}$ and approximately $5.4\times {10}^6$ $D\overline{D}$ events, we present a study of the decays $D^0\to {\pi }^{-}{e}^{+}{\nu }_e$, $D^0\to K^{-}{e}^{+}{\nu }_e$, $D^{+}\to {\pi }^0{e}^{+}{\nu }_e$, and $D^{+}\to {\overline{K}}^0{e}^{+}{\nu }_e$. Via a tagged analysis technique, in which one $D$ is fully reconstructed in a hadronic mode, partial rates for semileptonic decays by the other $D$ are measured in several $q^2$ bins. We fit these rates using several form factor parametrizations and report the results, including form factor shape parameters and the branching fractions $\mathcal{B}(D^0\to {\pi }^{-}{e}^{+}{\nu }_e)=(0.288\pm 0.008\pm 0.003)\%$, $\mathcal{B}(D^0\to K^{-}{e}^{+}{\nu }_e)=(3.50\pm 0.03\pm 0.04)\%$, $\mathcal{B}(D^{+}\to {\pi }^0{e}^{+}{\nu }_e)=(0.405\pm 0.016\pm 0.009)\%$, and $\mathcal{B}(D^{+}\to {\overline{K}}^0{e}^{+}{\nu }_e)=(8.83\pm 0.10\pm 0.20)\%$, where the first uncertainties are statistical and the second are systematic. Taking input from lattice quantum chromodynamics, we also find $|V_{cd}|=0.234\pm 0.007\pm 0.002\pm 0.025$ and $|V_{cs}|=0.985\pm 0.009\pm 0.006\pm 0.103$, where the third uncertainties are from lattice quantum chromodynamics.