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 $|V_{ub}/V_{cb}|$.

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

References in corpus (4)

• Implications of the $B\to X\ell {\bar{\nu }}_{\ell }$ lepton spectrum for heavy quark physics
• The Extraction of $V_{ub}$ from Inclusive B Decays and the Resummation of End Point Logs
• Perturbative corrections to zero recoil inclusive $B$ decay sum rules
• Ratios of $B$ and $D$ Meson Decay Constants in Relativistic Quark Model

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• Phenomenological Profiles of the Inclusive Hadron Spectra in the Decay $B\to X_s{\ell }^{+}{\ell }^{-}$
• The gluonic B and J/psi decays into the eta' meson
• Motion of b-quark inside B meson: the Parton Model vs. the ACCMM Model
• Heavy-quark binding and kinetic energies in heavy-light mesons and the constituent quark model
• Determination of HQET parameter λ_1 from Inclusive Semileptonic B Meson Decay Spectrum
• Hadronic Invariant Mass Spectrum in B -> X_u l nu Decay with Lepton Energy Cut
• A New Model-independent Method of Determining |V_{ub}/V_{cb}|
• Theory of Inclusive B Decays
• B_s(d) - bar B_s(d) mixing constraints on flavor changing decays of t and b quarks