Average Kinetic Energy of Heavy Quark in Semileptonic B Decay

Abstract

Within the ACCMM model the average kinetic energy of heavy quark in a heavy-light meson is calculated as $⟨{\mathbf{p}}^2⟩=\frac{3}{2}{p_{{}_F}}^2$, solely from the fact that the Gaussian momentum probability distribution has been taken in the ACCMM model. Therefore, the Fermi momentum parameter $p_{{}_F}$ of the ACCMM model is not a truly free parameter, but is closely related to the average kinetic energy of heavy quark, which is theoretically calculable in principle. In this context, we determine $p_{{}_F}$ by comparing the theoretical prediction of the ACCMM model with the model independent lepton energy spectrum of $B\to e\nu X$ from the recent CLEO analysis, and find that $p_{{}_F}=0.54\pm {}_{0.15}^{0.16}$ GeV. We also calculate $p_{{}_F}$ in the relativistic quark model by applying the quantum mechanical variational method, and obtained $p_{{}_F}=0.5\sim 0.6$ GeV. We show the correspondences between the relativistic quark model and the heavy quark effective theory. We then clarify the importance of the value of $p_{{}_F}$ in the determination of $|V_{ub}/V_{cb}|$.

Comments: 23 pages(LaTeX), 2 Postscript figures, uses aps.sty