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Measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msub><mml:mi>ν</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:math>differential decay branching fraction as a function of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:…
Based on a sample of 500 million ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}c\overline{c}$ events recorded by the BABAR detector at c.m. energies of close to 10.6 GeV, we report on a study of the decay ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e}$. We measure the ratio of branching fractions, ${R}_{D}=\mathcal{B}({D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e})/\mathcal{B}({D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})=0.0713\ifmmode\pm\else\textpm\fi{}0.001{7}_{\text{stat}}\ifmmode\pm\else\textpm\fi{}0.002{4}_{\text{syst}}$, and use the present world average for $\mathcal{B}({D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})$ to obtain $\mathcal{B}({D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e})=(2.770\ifmmode\pm\else\textpm\fi{}0.06{8}_{\text{stat}}\ifmmode\pm\else\textpm\fi{}0.09{2}_{\text{syst}}\ifmmode\pm\else\textpm\fi{}0.03{7}_{\text{ext}})\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3}$ …