Implications of the $B\to X\ell {\bar{\nu }}_{\ell }$ lepton spectrum for heavy quark physics

Abstract

The shape of the lepton spectrum in inclusive semileptonic $B\to X\ell {\bar{\nu }}_{\ell }$ decay is sensitive to matrix elements of the heavy quark effective theory, $\bar{\Lambda }$ and ${\lambda }_1$. From CLEO data we extract $\bar{\Lambda }=0.39\pm 0.11$GeV and ${\lambda }_1=-0.19\pm 0.10{\mathrm{GeV}}^2$, where the uncertainty is the $1\sigma$ statistical error only. Systematic uncertainties are discussed. These values for $\bar{\Lambda }$ and ${\lambda }_1$ are used to determine $|V_{cb}|$ and the $\overline{\mathrm{MS}}$ bottom and charm quark masses. We discuss the theoretical uncertainties related to order $({\Lambda }_{\mathrm{QCD}}/m_b{)}^3$ effects and higher orders in the perturbative expansion.

Comments: 10 pages revtex + one figure. Corrections from secondary leptons included, that affect the numerical results. Thus the central values become $\bar{\Lambda }=0.39\pm 0.11GeV$ and ${\lambda }_1=-0.19\pm 0.10Ge{V}^2$