Improved measurements of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>meson semileptonic decays to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>K</mml:mi></mml:math>mesons

Using the entire CLEO-c $\ensuremath{\psi}(3770)\ensuremath{\rightarrow}D\overline{D}$ event sample, corresponding to an integrated luminosity of $818\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ and approximately $5.4\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $D\overline{D}$ events, we present a study of the decays ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e}$, ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e}$, ${D}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{e}^{+}{\ensuremath{\nu}}_{e}$, and ${D}^{+}\ensuremath{\rightarrow}{\overline{K}}^{0}{e}^{+}{\ensuremath{\nu}}_{e}$. 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 $\mathcal{B}({D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e})=(0.288\ifmmode\pm\else\textpm\fi{}0.008\ifmmode\pm\else\textpm\fi{}0.003)%$, $\mathcal{B}({D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e})=(3.50\ifmmode\pm\else\textpm\fi{}0.03\ifmmode\pm\else\textpm\fi{}0.04)%$, $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{e}^{+}{\ensuremath{\nu}}_{e})=(0.405\ifmmode\pm\else\textpm\fi{}0.016\ifmmode\pm\else\textpm\fi{}0.009)%$, and $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{\overline{K}}^{0}{e}^{+}{\ensuremath{\nu}}_{e})=(8.83\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.20)%$, where the first uncertainties are statistical and the second are systematic. Taking input from lattice quantum chromodynamics, we also find $|{V}_{cd}|=0.234\ifmmode\pm\else\textpm\fi{}0.007\ifmmode\pm\else\textpm\fi{}0.002\ifmmode\pm\else\textpm\fi{}0.025$ and $|{V}_{cs}|=0.985\ifmmode\pm\else\textpm\fi{}0.009\ifmmode\pm\else\textpm\fi{}0.006\ifmmode\pm\else\textpm\fi{}0.103$, where the third uncertainties are from lattice quantum chromodynamics.