Abstract
We study the three-flavor Nambu–Jona-Lasinio model with various regularization procedures. We perform parameter fitting in each regularization and apply the obtained parameter sets to evaluate various physical quantities, several light meson masses, decay constant and the topological susceptibility. The model parameters are adopted even at very high cutoff scale compare to the hadronic scale to study the asymptotic behavior of the model. It is found that all the regularization methods except for the dimensional one actually lead reliable physical predictions for the kaon decay constant, sigma meson mass and topological susceptibility without restricting the ultra-violet cutoff below the hadronic scale.
Highlights
Nonet mesons are interesting composite hadronic objects which have been seriously studied in theoretical and experimental particle physics
We note that the result in the 3D case is the closest to the one by the lattice quantum chromodynamics (QCD) simulations, and the curves in the 4D, PV and PT enter the consistent region with lattice QCD for high, while the dimensional regularizations (DR) does not touch the gray region
In this paper we have applied various regularization procedures to the NJL model carried out the meticulous parameter fitting
Summary
Nonet mesons are interesting composite hadronic objects which have been seriously studied in theoretical and experimental particle physics. The most reliable approach is to consider the discretized version of QCD, called the lattice QCD, whose technologies are developing day by day It is, still difficult to study hadrons from the first principle, so the approaches by using some effective models become one of our options. The model predictions inescapably depend on the regularization procedures. The model shows parameter dependence in each regularization method. It is to be noted that the model has non-negligible parameter dependence even within the same regularization procedure [10]. For the sake of seeing the regularization and parameter dependence on the physical quantities, in this article, we shall perform the systematical parameter fitting in the three flavor model. Appendix shows the explicit equations for the meson properties and topological susceptibility
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