Measurement of the $D^0\to {\pi }^{-}{e}^{+}{\nu }_e$ differential decay branching fraction as a function of $q^2$ and study of form factor parameterizations

Abstract

Based on a sample of 500 million $e^{+}{e}^{-}\to c\bar{c}$ events recorded by the BaBar detector at c.m. energies of close to 10.6 GeV, we report on a study of the decay $D^0\to {\pi }^{-}{e}^{+}{\nu }_e$. We measure the ratio of branching fractions $R_D=\mathcal{B}(D^0\to {\pi }^{-}{e}^{+}{\nu }_e)/\mathcal{B}(D^0\to K^{-}{\pi }^{+})=0.0713\pm 0.0017_{stat.}\pm 0.0024_{syst.}$, and use the present world average for $\mathcal{B}(D^0\to K^{-}{\pi }^{+})$ to obtain $\mathcal{B}(D^0\to {\pi }^{-}{e}^{+}{\nu }_e)=(2.770\pm 0.068_{stat.}\pm 0.092_{syst.}\pm 0.037_{ext.})\times 10^{-3}$ where the third error accounts for the uncertainty on the branching fraction for the reference channel. The measured dependence of the differential branching fraction on $q^2$, the four-momentum transfer squared between the $D$ and the $\pi$ meson, is compared to various theoretical predictions for the hadronic form factor, $f_{+,D}^{\pi }(q^2)$, and the normalization $|V_{cd}|\times f_{+,D}^{\pi }(q^2=0)=0.1374\pm 0.0038_{stat.}\pm 0.0022_{syst.}\pm 0.0009_{ext.}$ is extracted from a fit to data. Using the most recent LQCD prediction of $f_{+,D}^{\pi }(q^2=0)=0.666\pm 0.029$, we obtain $|V_{cd}|=0.206\pm 0.007_{exp.}\pm 0.009_{\mathrm{LQCD}}$. Assuming instead, $|V_{cd}|=|V_{us}|=0.2252\pm 0.0009$, we obtain $f_{+,D}^{\pi }(q^2=0)=0.610\pm 0.020_{exp.}\pm 0.005_{ext.}$. The $q^2$ dependence of $f_{+,D}^{\pi }(q^2)$ is compared to a variety of multi-pole parameterizations. This information is applied to $B^0\to {\pi }^{-}{e}^{+}{\nu }_e$ decays and, combined with an earlier $B^0\to {\pi }^{-}{e}^{+}{\nu }_e$ measurement by BaBar, is used to derive estimates of $|V_{ub}|$.

arXiv comment28 pages, 15 postscript figures, submitted to Phys.Rev.D

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