Measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">B</mml:mi><mml:mi/><mml:mo>→</mml:mo><mml:mi/><mml:mi mathvariant="italic">D</mml:mi><mml:mi>ℓ</mml:mi><mml:mi mathvariant="italic">ν</mml:mi></mml:math>Branching Fractions and Form Factor

Using a sample of $3.3\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B$-meson decays collected with the CLEO detector at the Cornell Electron Storage Ring, we have studied ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{0}{\ensuremath{\ell}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$ and ${\overline{B}}^{0}\ensuremath{\rightarrow}{D}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$ decays, where ${\ensuremath{\ell}}^{\ensuremath{-}}$ can be either ${e}^{\ensuremath{-}}$ or ${\ensuremath{\mu}}^{\ensuremath{-}}$. We distinguish $B\ensuremath{\rightarrow}D\ensuremath{\ell}\ensuremath{\nu}$ from other $B$ semileptonic decays by examining the net momentum and energy of the particles recoiling against $D\ensuremath{-}\ensuremath{\ell}$ pairs. We find $\ensuremath{\Gamma}(B\ensuremath{\rightarrow}D\ensuremath{\ell}\ensuremath{\nu})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(14.1\ifmmode\pm\else\textpm\fi{}1.0\ifmmode\pm\else\textpm\fi{}1.2){\mathrm{ns}}^{\ensuremath{-}1}$ and derive branching fractions for ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{0}{\ensuremath{\ell}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$ and ${\overline{B}}^{0}\ensuremath{\rightarrow}{D}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$ of $(2.32\ifmmode\pm\else\textpm\fi{}0.17\ifmmode\pm\else\textpm\fi{}0.20)%$ and $(2.20\ifmmode\pm\else\textpm\fi{}0.16\ifmmode\pm\else\textpm\fi{}0.19)%$, respectively, where the uncertainties are statistical and systematic. We also investigate the $B\ensuremath{\rightarrow}D\ensuremath{\ell}\ensuremath{\nu}$ form factor and the implication of the result for $|{V}_{\mathrm{cb}}|$.