Scalar mesons in the Nambu--Jona-Lasinio model with 't Hooft interaction

We calculate the mass spectra of the pseudoscalar and scalar meson nonets in the Nambu–Jona-Lasinio model with the 't Hooft interaction. We obtain satisfactory result for the pseudoscalar mesons. For the scalar mesons, the 't Hooft interaction somewhat increases the values of the masses. However, it is not sufficient to explain the whole scalar mass spectrum. The situation could be improved for the $\sigma$ and $f_0$ mesons through mixing with the glueball state. For the description of the masses of $a_0$ and $\text{kstar}$ mesons, it is necessary to involve the other models. The strong decay widths of the scalar mesons are described.