SU(2) x SU(2) nonlocal quark model with confinement

Abstract.

The nonlocal version of the SU(2) x SU(2) symmetric four-quark interaction of the NJL type is considered. Each of the quark lines contains the form factors. These form factors remove the ultraviolet divergences in quark loops. The additional condition on the quark mass function m(p) ensures the absence of the poles in the quark propagator (quark confinement). The constituent-quark mass m(0) is expressed through the cut-off parameter $\Lambda$, $m(0) = \Lambda = 340$ MeV in the chiral limit. These parameters are fixed by the experimental value of the weak pion decay and allow us to describe the mass of the light scalar meson, the strong decay $\rho \rightarrow \pi \pi$ and the D/S ratio in the decay $a_1 \rightarrow \rho \pi$ in satisfactory agreement with the experimental data.