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 $\bar\Lambda=0.39\pm0.11\,$GeV and $\lambda_1=-0.19\pm0.10\,{\rm GeV}^2$, 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 $\overline{\rm MS}$ bottom and charm quark masses. We discuss the theoretical uncertainties related to order $(\Lambda_{\rm QCD}/m_b)^3$ effects and higher orders in the perturbative expansion.