Measurement of the moments of the hadronic invariant mass distribution in semileptonic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>decays

Abstract

Using 180 $\mathrm{p}{\mathrm{b}}^{\ensuremath{-}1}$ of data collected with the CDF II detector at the Tevatron, we measure the first two moments of the hadronic invariant mass-squared distribution in charmed semileptonic $B$ decays. From these we determine the nonperturbative Heavy Quark Effective Theory parameters $\ensuremath{\Lambda}$ and ${\ensuremath{\lambda}}_{1}$ used to relate the $B$ meson semileptonic branching ratio to the CKM matrix element $|{V}_{cb}|$. For a minimum lepton momentum of 0.7 GeV/$c$ in the $B$ rest frame we measure the first two moments of the ${D}^{**}\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\pi}$ component to be $⟨{m}_{{D}^{**}}^{2}⟩=(5.83\ifmmode\pm\else\textpm\fi{}{0.16}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.08}_{\mathrm{syst}})\text{ }\text{ }{\mathrm{GeV}}^{2}/{c}^{4}$ and $⟨({m}_{{D}^{**}}^{2}\ensuremath{-}⟨{m}_{{D}^{**}}^{2}⟩{)}^{2}⟩=(1.30\ifmmode\pm\else\textpm\fi{}{0.69}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.22}_{\mathrm{syst}})\text{ }\text{ }\mathrm{Ge}{\mathrm{V}}^{4}/{c}^{8}$. Combining these with the discrete mass terms from the $D$ and ${D}^{*}$ mesons, we find the total moments to be $⟨{M}_{{X}_{c}}^{2}⟩\ensuremath{-}{\overline{m}}_{D}^{2}=(0.467\ifmmode\pm\else\textpm\fi{}{0.038}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.068}_{\mathrm{syst}})\text{ }\text{ }\mathrm{Ge}{\mathrm{V}}^{2}/{c}^{4}$ and $⟨({M}_{{X}_{c}}^{2}\ensuremath{-}⟨{M}_{{X}_{c}}^{2}⟩{)}^{2}⟩=(1.05\ifmmode\pm\else\textpm\fi{}{0.26}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.13}_{\mathrm{syst}})\text{ }\text{ }\mathrm{Ge}{\mathrm{V}}^{4}/{c}^{8}$, where ${\overline{m}}_{D}$ is the spin-averaged $D$ mass. The systematic error is dominated by the uncertainties in the world-average branching ratios used to combine the $D$, ${D}^{*}$, and ${D}^{**}$ contributions. The analysis makes no assumptions about the shape or resonant structure of the ${D}^{**}\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\pi}$ invariant mass distribution.