Decay Constants and Semileptonic Decays of Heavy Mesons in Relativistic Quark Model

Abstract

We investigate the $B$ and $D$ mesons in the relativistic quark model by applying the variational method with the Gaussian wave function. We calculate the Fermi momentum parameter $p_{{}_F}$, and obtain $p_{{}_F}=0.50\sim 0.54$ GeV, which is almost independent of the input parameters, ${\alpha }_s$, $m_b$, $m_c$ and $m_{sp}$. We then calculate the ratio $f_B$/$f_D$, and obtain the result which is larger, by the factor of about 1.3, than $\sqrt{M_D/M_B}$ given by the naive nonrelativistic analogy. This result is in a good agreement with the recent Lattice calculations. We also calculate the ratio $(M_{B^{\ast }}-M_B)$/$(M_{D^{\ast }}-M_D)$. In these calculations the wave function at origin $\psi (0)$ is essential. We also determine $p_{{}_F}$ by comparing the theoretical prediction of the ACCMM model with the lepton energy spectrum of $B\to e\nu X$ from the recent ARGUS analysis, and find that $p_{{}_F}=0.27\pm {}_{0.27}^{0.22}$ GeV, when we use $m_c=1.5$ GeV. However, this experimentally determined value of $p_{{}_F}$ is strongly dependent on the value of input parameter $m_c$.

15 pages (Latex) (uses epsfig.sty, 1 figure appended as a uuencoded compressed ps-file)

References in corpus (9)

• QCD Predictions for Lepton Spectra in Inclusive Heavy Flavour Decays
• Inclusive Semileptonic B and Polarized Lambda_b Decays from QCD
• On the Motion of Heavy Quarks inside Hadrons: Universal Distributions and Inclusive Decays
• Sum Rules for Heavy Flavor Transitions in the SV Limit
• Next--to--Leading Order Corrections to Meson Masses in the Heavy Quark Effective Theory
• Heavy Quark Distribution Function in QCD and the AC${}^2$M${}^2$ Model
• Dependence of $|V_{ub}/V_{cb}|$ on Fermi momentum $p_{{}_F}$ in ACCMM model
• The ACCMM Model and the Heavy Quark Expansion
• New Approach for Measuring $|V_{ub}|$ at Future $B$-Factories

Cited by in corpus (12)

• Properties of $Q\bar{Q}$ mesons in non-relativistic QCD formalism
• Spectroscopy of Heavy Mesons Expanded in 1/m_Q
• Study of the leptonic decays of pseudoscalar $B,D$ and vector $B^{\ast },D^{\ast }$ mesons and of the semileptonic $B\to D$ and $B\to D^{\ast }$ decays
• Average Kinetic Energy of Heavy Quark and Virial Theorem
• Average Kinetic Energy of Heavy Quark in Semileptonic B Decay
• An Improved Analysis of Masses and Decay Constants of Heavy Flavour Mesons within Variational Approach
• Masses of Heavy-Light mesons with two loop static potential in a Variational approach
• Motion of b-quark inside B meson: the Parton Model vs. the ACCMM Model
• Determination of HQET parameter λ_1 from Inclusive Semileptonic B Meson Decay Spectrum
• Static and dynamic properties of hadronic systems with heavy quarks b and c
• A New Model-independent Method of Determining |V_{ub}/V_{cb}|
• Spectra and Decay Properties of Higher Lying $B_C$ Meson States