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    Measurement of lepton momentum moments in the decayB¯Xlν¯
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    Abstract:
    We measure the primary lepton momentum spectrum in $\overline{B}\ensuremath{\rightarrow}X\mathcal{l}\overline{\ensuremath{\nu}}$ decays, for ${p}_{\mathcal{l}}>~1.5\mathrm{GeV}/c$ in the B rest frame. From this, we calculate various moments of the spectrum. In particular, we find ${R}_{0}\ensuremath{\equiv}{\ensuremath{\int}}_{1.7\mathrm{GeV}}(d\ensuremath{\Gamma}{/dE}_{\mathrm{sl}}{)dE}_{\mathcal{l}}/{\ensuremath{\int}}_{1.5\mathrm{GeV}}(d\ensuremath{\Gamma}{/dE}_{\mathrm{sl}}{)dE}_{\mathcal{l}}=0.6187\ifmmode\pm\else\textpm\fi{}{0.0014}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.0016}_{\mathrm{sys}}$ and ${R}_{1}\ensuremath{\equiv}{\ensuremath{\int}}_{1.5\mathrm{GeV}}{E}_{\mathcal{l}}(d\ensuremath{\Gamma}{/dE}_{\mathrm{sl}}{)dE}_{\mathcal{l}}/{\ensuremath{\int}}_{1.5\mathrm{GeV}}(d\ensuremath{\Gamma}{/dE}_{\mathrm{sl}}{)dE}_{\mathcal{l}}=(1.7810\ifmmode\pm\else\textpm\fi{}{0.0007}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.0009}_{\mathrm{sys}})\mathrm{GeV}.$ We use these moments to determine non-perturbative parameters governing the semileptonic width. In particular, we extract the heavy quark expansion parameters $\overline{\ensuremath{\Lambda}}=(0.39\ifmmode\pm\else\textpm\fi{}{0.03}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.06}_{\mathrm{sys}}\ifmmode\pm\else\textpm\fi{}{0.12}_{\mathrm{th}})\mathrm{GeV}$ and ${\ensuremath{\lambda}}_{1}=(\ensuremath{-}0.25\ifmmode\pm\else\textpm\fi{}{0.02}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.05}_{\mathrm{sys}}\ifmmode\pm\else\textpm\fi{}{0.14}_{\mathrm{th}}){\mathrm{GeV}}^{2}.$ The theoretical constraints used are evaluated through order ${1/M}_{B}^{3}$ in the non-perturbative expansion and ${\ensuremath{\beta}}_{0}{\ensuremath{\alpha}}_{s}^{2}$ in the perturbative expansion. We use these parameters to extract $|{V}_{\mathrm{cb}}|$ from the world average of the semileptonic width and find $|{V}_{\mathrm{cb}}|=(40.8\ifmmode\pm\else\textpm\fi{}{0.5}_{{\ensuremath{\Gamma}}_{\mathrm{sl}}}\ifmmode\pm\else\textpm\fi{}{0.4}_{({\ensuremath{\lambda}}_{1},\overline{\ensuremath{\Lambda}}{)}_{\mathrm{exp}}}\ifmmode\pm\else\textpm\fi{}{0.9}_{\mathrm{th}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}.$ In addition, we extract the short range b-quark mass ${m}_{b}^{1\mathrm{S}}=(4.82\ifmmode\pm\else\textpm\fi{}{0.07}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{0.11}_{\mathrm{th}})\mathrm{GeV}{/c}^{2}.$ Finally, we discuss the implications of our measurements for the theoretical understanding of inclusive semileptonic processes.
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