Hadronic Mass Moments in Inclusive Semileptonic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">B</mml:mi></mml:math>Meson Decays

Abstract

We have measured the first and second moments of the hadronic mass-squared distribution in $B\ensuremath{\rightarrow}{X}_{c}\ensuremath{\ell}\ensuremath{\nu}$, for ${P}_{\mathrm{lepton}}&gt;1.5\mathrm{GeV}/c$. We find $〈{M}_{X}^{2}\ensuremath{-}{\overline{M}}_{D}^{2}〉\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.251\ifmmode\pm\else\textpm\fi{}0.066{\mathrm{GeV}}^{2}$, $\mathbf{〈}({M}_{X}^{2}\ensuremath{-}〈{M}_{X}^{2}〉{)}^{2}\mathbf{〉}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.576\ifmmode\pm\else\textpm\fi{}0.170{\mathrm{GeV}}^{4}$, where ${\overline{M}}_{D}$ is the spin-averaged $D$ meson mass. From that first moment and the first moment of the photon energy spectrum in $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$, we find the heavy quark effective theory parameter ${\ensuremath{\lambda}}_{1}$ (in the modified minimal subtraction renormalization scheme, to order ${1/M}_{B}^{3}$ and ${\ensuremath{\beta}}_{0}{\ensuremath{\alpha}}_{s}^{2}$) to be $\ensuremath{-}0.24\ifmmode\pm\else\textpm\fi{}0.11{\mathrm{GeV}}^{2}$. Using these first moments and the $B$ semileptonic width, and assuming parton-hadron duality, we obtain $|{V}_{\mathrm{cb}}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.0404\ifmmode\pm\else\textpm\fi{}0.0013$.