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

Abstract

Succeeding in predicting 0^+ and 1^+ states of D and D_s heavy mesons by our semi-relativistic quark potential model, we examine a method how to construct 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 show how effective this is, we apply the formulation to calculate the semileptonic weak form factors out of the rest frame wave functions of heavy mesons and numerically calculate the dynamical 1/m_Q corrections to those for the process B-bar -> D^{(*)}\ell\nu based on our model for heavy mesons. It is shown that nonvanishing expressions for \rho_1(\omega)=\rho_2(\omega) and \rho_3(\omega)=\rho_4(\omega)=0 are obtained in a special Lorentz frame, where \rho_i(\omega) are the parameters used in the Neubert-Rieckert decomposition of form factors. Various values of form factors are estimated, which are compatible with recent experimental data as well as other theoretical calculations.