Application of a generalized Nambu-Jona-Lasinio model to the calculation of the properties of scalar mesons and nuclear matter - art. no. 025209

In this work we demonstrate the range of application of our generalized Nam bu-Jona-Lasinio (NJL) model. We discuss the scalar-isoscalar mesons that ar e thought to have a q (q) over bar structure and also consider some propert ies of nuclear matter. The spectrum of scalar-isoscalar mesons provides som e insight into the sigma models that may be used to describe the dynamics o f pseudoscalar and scalar mesons. Some authors have suggested that the lowe st q (q) over bar 0(++) state is the f(0)(1370). [The f(0)(400-1200) that n ow appears in the data tables may be generated dynamically in pi-pi scatter ing and is not a "preexisting" state of the spectrum.] The f(0)(980) and a( 0)(980) are often designated as K-(K) over bar molecules. However, recent w ork does not support that assignment. Since there is no low-lying scalar st ate, the model of choice in describing pseudoscalar meson dynamics is the n onlinear sigma model. However, there are a number of applications of the Na mbu-Jona-Lasinio model in the study of nuclear matter properties that can b e described in terms of the linear sigma model. In the linear sigma model t here is a low-mass sigma meson, whose effects would be generated dynamicall y in the nonlinear model. While it is not necessary to ever introduce a low -mass sigma meson, we describe some calculations which may be interpreted i n terms of such a meson. That only represents a formal device, and no low-m ass sigma is to be found in experiment. However, the use of the low-mass si gma as an order parameter for partial restoration of chiral symmetry at fin ite density is quite consistent with the picture obtained in the applicatio n of QCD sum rules to the calculation of the nucleon self-energy in nuclear matter. We discuss such sum rules to show that the linear sigma model has some limited application if we consider only spacelike values of the sigma meson momentum. We also use our generalized NJL model to discuss the spectr um of scalar-isoscalar states under the assumption that the f(0)(1370) is t he 1 P-3(0) n (n) over bar state and the f(0)(1710) is the 1 P-3(0) s (s) o ver bar state before consideration of quarkonium-glueball mixing. That anal ysis allows us to provide a microscopic model of the two q (q) over bar sta tes used by Close and Kirk in their recent description of quarkonium-glueba ll mixing in which they obtain wave functions of the f(0)(1370), f(0)(1500) , and f(0)(1710) resonances. However, we also present an argument to show t hat the configuration assignments implied in the work of Close and Kirk are probably incorrect and that the standard scheme for the discussion of quar konium-glueball mixing needs modification.