Improved measurements of $D$ meson semileptonic decays to $\pi$ and $K$ mesons

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.

Figure 1

$M_{\mathrm{BC}}$ distributions in data (points), with fits (solid lines) and background contributions to fits (dotted lines). The vertical lines show the limits of the $M_{\mathrm{BC}}$ signal regions.

Figure 2

$U$ distributions in data (points) for $D^0\to {\pi }^{-}{e}^{+}{\nu }_e$, with fit results (histograms) showing signal (clear) and background components: $D^0\to {\rho }^{-}{e}^{+}{\nu }_e$ (darkest gray), $D^0\to K^{-}{e}^{+}{\nu }_e$ (lightest gray), other $D\overline{D}$ (medium gray), and non-$D\overline{D}$ (black).

Figure 3

$U$ distributions in data (points) for $D^0\to K^{-}{e}^{+}{\nu }_e$, with fit results (histograms) showing signal (clear) and background components: $D\overline{D}$ (gray) and non-$D\overline{D}$ (black).

Figure 4

$U$ distributions in data (points) for $D^{+}\to {\pi }^0{e}^{+}{\nu }_e$, with fit results (histograms) showing signal (clear) and background components: $D^{+}\to {\overline{K}}^0{e}^{+}{\nu }_e$ (light gray), other $D\overline{D}$ (dark gray), and non-$D\overline{D}$ (black).

Figure 5

$U$ distributions in data (points) for $D^{+}\to {\overline{K}}^0{e}^{+}{\nu }_e$, with fit results (histograms) showing signal (clear) and background components: $D\overline{D}$ (gray) and non-$D\overline{D}$ (black).

Figure 6

Partial rates for each semileptonic mode. The points show measurements in each tag mode; the histograms show the partial rates averaged over all tag modes.

Figure 7

Distributions of $\cos {\theta }_{We}$ (upper), the cosine of the angle between the virtual $W$ and the positron, positron momentum (middle) and hadron momentum (lower) in events satisfying $-60\mathrm{MeV}<U<60\mathrm{MeV}$. Signal and background shapes are taken from MC simulations and scaled using the parameters of the signal yield fits.

Figure 8

$f_{+}(q^2)$ comparison between isospin conjugate modes and with LQCD calculations [21]. The solid lines represent LQCD fits to the modified pole model [15]. The inner bands show LQCD statistical uncertainties, and the outer bands the sum in quadrature of LQCD statistical and systematic uncertainties.

Figure 9

Individual form factor fits to data (points) using two-parameter (dashed) and three-parameter (solid) series expansions.

Figure 10

Isospin-combined form factor fits to data (points) using two-parameter (dashed) and three-parameter (solid) series expansions.

Figure 11

Comparison of form factor fits for each semileptonic mode. The data (squares) and fits to the form factor parametrizations (histograms), including the simple pole model (long dash), modified pole model (short dash), and two-parameter series fit (dotted), are all normalized using the three-parameter fit result (solid line at unity).