What are the right values of $\bar \Lambda$ and the heavy quark kinetic energy?

Abstract

The values of two important parameters of the heavy quark effective theory,\, $\bar \Lambda$ and $\mu_\pi^2$ (the mean value of the heavy quark three momentum squared),\, have been determined recently in \cite {GKLW} from the precise CLEO data on the shape of the electron spectrum in semileptonic B meson decays. The values obtained in \cite{GKLW}: $\bar \Lambda=(0.55\pm 0.05)\,GeV,\, \mu_\pi^2=(0.35\pm 0.05)\,GeV^2,$ disagree with the result obtained earlier in \cite{CH} from the D meson semileptonic width. The purpose of this note is to show that the main reason for a disagreement is the secondary electron background present in the data,\, which influences strongly the extracted values of $\bar \lambda$ and $\mu_\pi^2$. We determine the amount of this background from the selfconsistency conditions,\, and subtract it out. As a result,\, the values of $\bar \Lambda$ and $\mu_\pi^2$ become a factor two smaller and agree with \cite{CH}.