Parametrization of a nonlocal, chiral quark model in the instantaneous three-flavor case. Basic formulas and tables

Abstract

In these notes we describe the basic formulation of the parametrization scheme for the instantaneous nonlocal chiral quark model in the three flavor case. We choose to discuss the Gaussian, Lorentzian-type, Woods-Saxon and sharp cutoff (NJL) functional forms of the momentum dependence for the formfactor of the separable interaction. The four parameters: light and strange quark mass, coupling strength (G_S) and range of the interaction (Lambda) have been fixed by the same phenomenological inputs: pion and kaon mass, pion decay constant and light quark mass in vacuum. The Wood-Saxon and Lorentzian-type formfactor is suitable for an interpolation between sharp cutoff and soft momentum dependence. Results are tabulated for applications in models of hadron structure and quark matter at finite temperatures and chemical potentials where separable models have proven successful.