Extended NJL Model for light and heavy mesons without q-qbar thresholds

We consider the NJL model as an effective quark theory to describe the interaction which is responsible for the quark flavor dynamics at intermediate energies. In addition to the usual ultraviolet cut-off which is necessary since the model is non-renormalizable, we also introduce an infrared cut-off which drops off the unknown confinement part of the quark interaction, which is believed to be less important for the flavor dynamics. The infrared cut-off eliminates all q-qbar thresholds, which plague the application of the usual NJL model beyond low-energy pion physics. We apply this two-cut-off prescription to the extended NJL model with chiral and heavy quark symmetries proposed recently by us. We find a satisfactoring description even of the heavy mesons with spin/parity J/P = (0+, 1+). Furthermore, the shape-parameters of the Isgur-Wise function are studied as a function of the residual heavy meson mass.