Measurement of the hadronic form factor inD0→K−e+νedecays

The shape of the hadronic form factor $f_{+}(q^2)$ in the decay $D^0\to K^{-}{e}^{+}{\nu }_e$ has been measured in a model independent analysis and compared with theoretical calculations. We use $75{\mathrm{fb}}^{-1}$ of data recorded by the BABAR detector at the PEP-II electron-positron collider. The corresponding decay branching fraction, relative to the decay $D^0\to K^{-}{\pi }^{+}$, has also been measured to be $R_D=\mathcal{B}(D^0\to K^{-}{e}^{+}{\nu }_e(\gamma ))/\mathcal{B}(D^0\to K^{-}{\pi }^{+}(\gamma ))=0.927\pm 0.007\pm 0.012$. From these results, and using the present world average value for $\mathcal{B}(D^0\to K^{-}{\pi }^{+})$, the normalization of the form factor at $q^2=0$ is determined to be $f_{+}(0)=0.727\pm 0.007\pm 0.005\pm 0.007$ where the uncertainties are statistical, systematic, and from external inputs, respectively.