Average kinetic energy of a heavy quark in semileptonicBdecay

Abstract

Within the ACCMM model the average kinetic energy of heavy quark in a heavy-light meson is calculated as hp, 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 ! eX from the recent CLEO analysis, and nd that p F = 0 : 51 0:08 0:07 GeV. We also calculate p F in the relativistic quark model by applying the quantum mechanical variational method, and obtained p F = 0 : 5 0 : 6 GeV. We show the correspondences between the relativistic quark model and the heavy quark eective theory. W e then clarify the importance of the value of p F in the determination of jV ub =V cb j.

Average kinetic energy of heavy quark and virial theorem

“…For the study of the bound state properties of hadrons which contain both heavy and light quarks like B-meson, it is appropriate to use the relativistic quark model [12,21], which is a potential model approach with relativistic kinematics.…”

“…However, Kapustin et al [11] showed later that this lower bound could be significantly weakened by higher order perturbative corrections. Previously we also calculated [12] the value of p 2 by applying the variational method to the relativistic Hamiltonian, and obtained p 2 = 0.44 GeV 2 .…”

Heavy-quark binding and kinetic energies in heavy-light mesons and the constituent quark model

“…However, we point out that the result −λ 1 = p 2 is characteristic of CQ models in which a non-relativistic interquark potential, which is more appropriate in case of heavy-heavy mesons, is adopted for the description of heavy-light mesons, as it has been done in Refs. [12,13] and [14]. The aim of this letter is indeed to show that in case of heavy-light mesons the CQ model (CQM) prediction for −λ 1 is sharply sensitive to relativistic effects in the CQ interaction, which may lead to substantial deviations from the non-relativistic expectation −λ 1 = p 2 .…”

“…Refs. [12,13]). However, we point out that the result −λ 1 = p 2 is characteristic of CQ models in which a non-relativistic interquark potential, which is more appropriate in case of heavy-heavy mesons, is adopted for the description of heavy-light mesons, as it has been done in Refs.…”

“…Refs. [12,13]), depending mainly on the specific value adopted for the (effective) running coupling constant, which governs directly the strength of the Coulomb-like interaction term c . However, the relativistic effects in the interquark c In the ISGW model [14] a local Cornell-type potential is adopted and the ground-state meson wave function is approximated by a gaussian ansätz, which yields p 2 ≃ 0.28 GeV 2 .…”