The Isgur-Wise function in a relativistic model for q Q system

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We use the Dirac equation with a ``(asymptotically free) Coulomb + (Lorentz scalar) linear '' potential to estimate the light quark wavefunction for q Q mesons in the limit mQ→ ∞. We use these wavefunctions to calculate the Isgur-Wise function ξ(v.v′) for orbital and radial ground states in the phenomenologically interesting range 1≤ v.v ′ ≤ 4. We find a simple expression for the zero-recoil slope, ξ ′ (1) =-1/2- ε² <rq²>/3, where ε is the energy eigenvalue of the light quark, which can be identified with the Λ parameter of the Heavy Quark Effective Theory. This result implies an upper bound of -1/2 for the slope ξ′ (1). Also, because for a very light quark q (q=u, d) the size √ <rq²> of the meson is determined mainly by the ``confining'' term in the potential (γ∘ σr), the shape of ξᵤ,d(v.v′) is seen to be mostly sensitive to the dimensionless ratio Λᵤ,d²/σ. We present results for the ranges of parameters 150 MeV < Λᵤ,d <600 MeV (Λₛ ≈ Λᵤ,d+100 MeV), 0.14 GeV² ≤ σ≤ 0.25 GeV² and light quark masses mᵤ, md ≈ 0, mₛ=175 MeV and compare to existing experimental data and other theoretical estimates. Fits to the data give: Λᵤ,d²/σ=4.8± 1.7, -ξ′ᵤ,d(1)=2.4± 0.7 and Vcb √ τB/1.48 ps=0.050± 0.008 [ARGUS '93]; Λᵤ,d²/σ= 3.4± 1.8, -ξ′ᵤ,d(1)=1.8± 0.7 and Vcb √ τB/1.48 ps=0.043± 0.008 [CLEO '93]; Λᵤ,d²/