$K\to 2\pi$ Decay in the Nambu-Jona-Lasinio Model

We study the $K\to 2\pi$ decays using the $U_L(3)\times U_R(3)$ version of the Nambu-Jona-Lasinio model with the effective $\mathrm{\Delta }S=1$ nonleptonic weak interaction. The $\mathrm{\Delta }I=3\mathrm{/}2$ amplitude is in reasonable agreement with experimental data. On the other hand, the calculated $\mathrm{\Delta }I=1\mathrm{/}2$ amplitudes strongly depend on the mass of the low-lying scalar-isoscalar $\sigma$ meson, and therefore give a strong constraint on the parameters of the model.