ISGUR-WISE FUNCTION IN A RELATIVISTIC MODEL FOR A Q(Q)OVER-BAR SYSTEM

We use the Dirac equation with a "(asymptotically free) Coulomb + (Lorentz scalar) linear" potential to estimate the light quark wave function for qQ̄ mesons in the limit mQ→. We use these wave functions to calculate the Isgur-Wise function ξ(υ) for orbital and radial ground states in the phenomenologically interesting range 1 ≤υυ′;≤4. We find a simple expression for the zero-recoil slope, ξ′;(1)=-1/2-ε2/3, where ε is energy eigenvalue of the light quark, which can be identified with the Λ̄ 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 of the meson is determined mainly by the "confining" term in the potential (γ0σr), the shape of ξu,d(υυ′;) is seen to be the most sensitive to the dimensionless ratio Λ̄u,d2/σ. We present results for the ranges of parameters 150 MeV<Λ̄u,d<600 MeV (Λ̄sΛ̄u,d+100 MeV), 0.14 GeV2≤σ≤0.25 GeV2 and light quark masses mu,md0, ms=175 MeV and compare to existing experimental data and other theoretical estimates. Fits to the data give Λ̄u,d2/σ=4.8±1.7, -ξ′;u,d(1)=2.4±0.7, and |Vcb|τB/1.48 ps=0.50±0.008 [ARGUS 1993]; Λ̄u,d2/σ=3.3±1.2, -ξu,d′;(1)=1.8±0.5, and |Vcb|τB/1.48 ps=0.043±0.005 [CLEO 1993]; Λ̄u,d2/σ=2.0±0.7, -ξu,d′;(1)=1.3±0.3, and |Vcb|F(1)=0.037±0.002 [CLEO 1994] [existing theoretical estimates for F(1) fall in the range 0.86<F(1)<1.01]. Our model seems to favor the CLEO 1994 data set in two respects: the fits are better and the resulting ranges for the model parameters (Λ̄u,d, σ) are more in line with independent theoretical estimates. © 1995 The American Physical Society.