  In this talk results of the study of the $D^0 \to \pi^- e^+ \nu$ decay
channel, recorded by the BaBar detector at the c.m. energy close to 10.6 GeV,
are reported. The branching fraction of this channel is measured relative to
the $D^0 \to K^- \pi^+$ decay. The hadronic form factor, $f_{+,D}^{\pi}(q^2)$,
function of $q^2$, the four momentum transfer squared between the $D$ and the
$\pi$ mesons, is compared to various theoretical predictions, and the
normalization $V_{cd} \times f_{+,D}^{\pi}(q^2=0)$ is extracted from a fit to
data. Results are compared with Lattice QCD calculations. A new multipole model
is applied which makes use of present information of resonant states
contributing to the form factor. With the understanding of the
$f_{+,D}^{\pi}(q^2)$ form factor, and provided the relation between the $D^0
\to \pi^- e^+ \nu$ and $B^0 \to \pi^- e^+ \nu$ decay widths at the same pion
energy, the CKM matrix element $V_{ub}$ is determined and compared to recent
measurements. This method of extracting $V_{ub}$ will become competitive with
new Lattice QCD calculations of the ratio of form factors.
