The Isgur-Wise function in a relativistic model for $q\bar{Q}$ system

Abstract

We use the Dirac equation with a ``(asymptotically free) Coulomb + (Lorentz scalar) linear '' potential to estimate the light quark wavefunction for $q\bar{Q}$ mesons in the limit $m_Q\to \infty$. We use these wavefunctions to calculate the Isgur-Wise function $\xi (v.v^{\prime })$ for orbital and radial ground states in the phenomenologically interesting range $1\le v.v^{\prime }\le 4$. We find a simple expression for the zero-recoil slope, ${\xi }^{\prime }(1)=-1/2-{\epsilon }^2<{r_q}^2>/3$, where $\epsilon$ is the energy eigenvalue of the light quark, which can be identified with the $\bar{\Lambda }$ parameter of the Heavy Quark Effective Theory. This result implies an upper bound of $-1/2$ for the slope ${\xi }^{\prime }(1)$. Also, because for a very light quark $q(q=u,d)$ the size $\sqrt{<{r_q}^2>}$ of the meson is determined mainly by the ``confining'' term in the potential $({\gamma }_{\circ }\sigma r)$, the shape of ${\xi }_{u,d}(v.v^{\prime })$ is seen to be mostly sensitive to the dimensionless ratio ${\bar{\Lambda }}_{u,d}^2/\sigma$. We present results for the ranges of parameters $150MeV<{\bar{\Lambda }}_{u,d}<600MeV$ $({\bar{\Lambda }}_s\approx {\bar{\Lambda }}_{u,d}+100MeV)$, $0.14{GeV}^2\le \sigma \le 0.25{GeV}^2$ and light quark masses $m_u,m_d\approx 0,m_s=175MeV$ and compare to existing experimental data and other theoretical estimates. Fits to the data give: ${{\bar{\Lambda }}_{u,d}}^2/\sigma =4.8\pm 1.7$, $-{\xi }_{u,d}^{\prime }(1)=2.4\pm 0.7$ and $|V_{cb}|\sqrt{\frac{{\tau }_B}{1.48ps}}=0.050\pm 0.008$ [ARGUS '93]; ${{\bar{\Lambda }}_{u,d}}^2/\sigma =3.4\pm 1.8$, $-{\xi }_{u,d}^{\prime }(1)=1.8\pm 0.7$ and $|V_{cb}|\sqrt{\frac{{\tau }_B}{1.48ps}}=0.043\pm 0.008$ [CLEO '93]; ${\barΛ_{u,d}}^2/

22 pages, Latex, 4 figures (not included) available by fax or via email upon request

References in corpus (9)

• Heavy Quark Symmetry
• Measurement of the B -> D^* l nu Branching Fractions and |Vcb|
• $|V_{cb}|$ from OPE Sum Rules for Heavy Flavor Transitions
• Higher Order $1/m$ Corrections at Zero Recoil
• A New Determination of M_b Using Lattice QCD
• Isgur-Wise Functions from the Mit Bag Model
• Quark Model Form Factors for Heavy Quark Effective Theory
• $D_s$ Lifetime, $m_b$, $m_c$ and $|V_{cb}|$ in the Heavy Quark Expansion
• Light Quark Dependence of the Isgur-Wise Function from QCD Sum rules

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• Anomalous Kinetics of Hard Charged Particles: Dynamical Renormalization Group Resummation
• Weak Decays in the light--front Quark Model
• Isgur-Wise function in a QCD potential model with coulombic potential as perturbation
• Semileptonic form factors - a model-independent approach
• Decay constants and mixing parameters in a relativistic model for q\barQ system
• Bounds on the slope and curvature of Isgur-Wise function in a QCD inspired quark model
• On the bounds for the curvature and higher derivatives of the Isgur-Wise function
• Study on the structure of the four-quark states in terms of the Born-Oppenheimer approximation