Parametrization solver

Some parameters of the (P)NJL model can be fitted to meson properties in the vacuum. This program does this by solving the equations for the pion mass, the pion decay constant and the kaon mass. For further information, see [1]. Note, however, that the kaon-mass formula used here is:

kaon mass formula

The symbols appearing in this expression are defined in [1]. In order to solve the system of equations it is necessary to specify the regularization method, i.e., the instantaneous form factor in momentum space. One way to fix the form factor is to tune it such that the constituent quark mass, M(p=0), and the chiral condensate has sound values.

Regularization
Form factor:
Λ: MeV
α: (for the lorentzian form factor)


Charts

These charts illustrate the relation between the smoothness of the lorentzian form factor, α, the constituent quark mass, Mq(p=0), and the other quantities. The cutoff form factor corresponds to the limit of inifite α. These charts were produced by varying Λ between 600 MeV and 800 MeV.

G_S Lambda Chiral condensate m_q m_s

References

[1] H. Grigorian, Parametrization of a nonlocal, chiral quark model in the instantaneous three-flavor case: Basic formulas and tables, Phys. Part. Nucl. Lett. 4, 223 (2007); hep-ph/0602238, SPIRES.