Quark Condensates and Momentum-Dependent Quark Masses in a Nonlocal   Nambu--Jona-Lasinio Model
  The Nambu--Jona-Lasinio (NJL) model has been extensively studied by many researchers. In previous work we have generalized the NJL model to include a covariant model of confinement. In the present work we consider further modification of the model so as to reproduce the type of Euclidean-space momentum- dependent quark mass values obtained in lattice simulations of QCD. This may be done by introducing a nonlocal interaction, while preserving the chiral symmetry of the Lagrangian. In other work on nonlocal models, by other researchers, the momentum dependence of the quark self-energy is directly related to the regularization scheme. In contrast, in our work, the regularization is independent of the nonlocality we introduce. It is of interest to note that the value of the condensate ratio, $<\bar{s}s>/<\bar{u}d>$, is about 1.7 when evaluated using chiral perturbation theory and is only about 1.1 in standard applications of the NJL model. We find that our nonlocal model can reproduce the larger value of the condensate ratio when reasonable values are used for the strength of the 't Hooft interaction. (In an earlier study of the $\eta$(547) and $\eta$'(958) mesons, we found that use of the larger value of the condensate ratio led to a very good fit to the mixing angles and decay constants of these mesons.) We also study the density dependence of both the quark condensate and the momentum-dependent quark mass values. Without the addition of new parameters, we reproduce the density dependence of the condensate given by a well-known model- independent expression valid for small baryon density. 
Bing He, Hu Li, Qing Sun, and C.M. Shakin