Study of the semileptonic decay mode $D^0$→$K^{\mathrm{-}}$$e^{+}$${\nu }_e$

We present an analysis of the exclusive semileptonic decay mode $D^0$→$K^{\mathrm{-}}$ $e^{+}$ ${\nu }_e$. We have measured the ratio of decay rates .11(syst), which corresponds to a $D^0$→$K^{\mathrm{-}}$ $e^{+}$ ${\nu }_e$ branching fraction of (3.8±0.5±0.6)%. Combining our result with a measurement of the $D^0$ lifetime, we find .1±1.4)×${10}^{10}$ ${\mathrm{s}}^{\mathrm{-}1}$. We have also measured the vector form factor $f_{+}$(t) and find that it is consistent with the single-pole form where the pole mass &=2.11 GeV/$c^2$.