Determination of the Branching Fraction for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mi>ℓ</mml:mi><mml:mi>ν</mml:mi></mml:math>Decays and of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo>|</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:math>from Hadronic-Mass and Lepton-Energy Moments

We determine the inclusive $B\ensuremath{\rightarrow}{X}_{c}\ensuremath{\ell}\ensuremath{\nu}$ branching fraction, ${\mathcal{B}}_{c\ensuremath{\ell}\ensuremath{\nu}}$, the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cb}|$, and other heavy-quark parameters from a simultaneous fit to moments of the hadronic-mass and lepton-energy distributions in semileptonic $B$-meson decays, measured as a function of the lower limit on the lepton energy, using data recorded with the BABAR detector. Using heavy-quark expansions (HQEs) to order $1/{m}_{b}^{3}$, we extract ${\mathcal{B}}_{ce\ensuremath{\nu}}=(10.61\ifmmode\pm\else\textpm\fi{}{0.16}_{\mathrm{e}\mathrm{x}\mathrm{p}}\ifmmode\pm\else\textpm\fi{}{0.06}_{\mathrm{H}\mathrm{Q}\mathrm{E}})%$ and $|{V}_{cb}|=(41.4\ifmmode\pm\else\textpm\fi{}{0.4}_{\mathrm{e}\mathrm{x}\mathrm{p}}\ifmmode\pm\else\textpm\fi{}{0.4}_{\mathrm{H}\mathrm{Q}\mathrm{E}}\ifmmode\pm\else\textpm\fi{}{0.6}_{\mathrm{t}\mathrm{h}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. The stated errors refer to the experimental, HQE, and additional theoretical uncertainties.

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