Hadronic spectral moments in semileptonicBdecays with a lepton energy cut

Abstract

We compute the first two moments $〈{(s}_{H}\ensuremath{-}{m}_{D}^{2}{)}^{1,2}〉$ of the final hadronic invariant mass in the inclusive decay $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{c}\mathcal{l}\overline{\ensuremath{\nu}},$ in the presence of a cut ${E}_{\mathcal{l}}^{\mathrm{min}}$ on the charged lepton energy. These moments may be measured directly by experiments at the $\ensuremath{\Upsilon}(4S)$ using the neutrino reconstruction technique, which requires such a cut. Measurement of these moments will place constraints on the nonperturbative parameters $\overline{\ensuremath{\Lambda}}$ and ${\ensuremath{\lambda}}_{1},$ which are relevant for extracting the quark masses ${m}_{b}$ and ${m}_{c},$ as well as the CKM angle ${V}_{\mathrm{cb}}.$ We include terms of order ${\ensuremath{\alpha}}_{s}^{2}{\ensuremath{\beta}}_{0}$ and ${1/m}_{b}^{3}$ in the operator product expansion, and use the latter to estimate the theoretical uncertainty in the extraction of $\overline{\ensuremath{\Lambda}}$ and ${\ensuremath{\lambda}}_{1}.$