Construction of Lorentz-Invariant Amplitudes from Rest-Frame Wave Functions in HQET: Application to the Isgur-Wise Function

Succeeding in predicting 0+ and 1+ states of D and Ds heavy mesons with our semi-relativistic quark potential model, we examine a method for constructing Lorentz-invariant scattering amplitudes and/or decay widths and develop a formulation to calculate Lorentz-boosted ones given the rest-frame wave functions in our model. To illustrate the effectiveness of our method, we apply the formulation to the problem of calculating the semileptonic weak form factors from the rest-frame wave functions of heavy mesons and numerically calculate the dynamical 1/mQ corrections to those for the process B → D(*)ℓ v based on our model of heavy mesons. It is shown that nonvanishing expressions for ρ1(ω) = ρ2(ω) and ρ3(ω) = ρ4(ω)= 0 are obtained in a special Lorentz frame, where ρi(ω) are the parameters used in the Neubert-Rieckert decomposition of form factors. Various values of form factors are estimated. These values are compatible with recent experimental data as well as other theoretical calculations.