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Based on a sample of 500 million $e^+e^- \to c\bar c$ events recorded by theBaBar detector at c.m. energies of close to 10.6 GeV, we report on a study ofthe decay $D^0 \to \pi^- e^+ \nu_e$. We measure the ratio of branchingfractions $R_D = {\cal B}(D^0 \to \pi^- e^+ \nu_e)/{\cal B}(D^0 \to K^- \pi^+)= 0.0713 \pm 0.0017_{stat.} \pm 0.0024_{syst.}$, and use the present worldaverage for ${\cal B}(D^0 \to K^- \pi^+)$ to obtain ${\cal B}(D^0 \to \pi^- e^+\nu_e) = (2.770 \pm 0.068_{{\rm stat.}} \pm 0.092_{{\rm syst.}} \pm 0.037_{{\rmext.}})\times 10^{-3}$ where the third error accounts for the uncertainty onthe branching fraction for the reference channel. The measured dependence ofthe differential branching fraction on $q^2$, the four-momentum transfersquared between the $D$ and the $\pi$ meson, is compared to various theoreticalpredictions for the hadronic form factor, $f_{+,D}^{\pi}(q^2)$, and thenormalization $|V_{cd}| \times f_{+,D}^{\pi}(q^2=0)=0.1374\pm0.0038_{{\rmstat.}} \pm0.0022_{{\rm syst.}} \pm0.0009_{{\rm ext.}}$ is extracted from a fitto data. Using the most recent LQCD prediction of $f_{+,D}^{\pi}(q^2=0)=0.666\pm 0.029$, we obtain $|V_{cd}|=0.206 \pm 0.007_{\rm exp.} \pm 0.009_{\rmLQCD}$. Assuming instead, $|V_{cd}|=|V_{us}|=0.2252 \pm 0.0009$, we obtain$f_{+,D}^{\pi}(q^2=0)=0.610 \pm 0.020_{\rm exp.} \pm 0.005_{\rm ext.}$. The$q^2$ dependence of $f_{+,D}^{\pi}(q^2)$ is compared to a variety of multi-poleparameterizations. 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 byBaBar, is used to derive estimates of $|V_{ub}|$.

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