$\sigma$ and $\kappa$ mesons as broad dynamical resonances in one-meson-exchange model

The existences of broad scalar $\mathrm{\sigma (600)}$ and $\mathrm{\kappa (700)}$ mesons have been discussed intensively in the experimental and theoretical studies on $\mathrm{\pi \pi }$ and $\mathrm{\pi K}$ scatterings. By using chiral perturbation model, J. Oller, A. G\'omez and J. R. Pel\'aez confirmed the existence of these mesons as dynamical resonances. In meson-exchange models, their existence has not been established yet. In this talk, using the quasi-potential of meson-exchange model and Lippmann-Schwinger equation, we determine the T and S -matrices, from which we could find the positions of poles in physical amplitudes in the complex E-plane. With the full treatment of meson-meson interactions ($\mathrm{\pi \pi -\pi K-\pi \eta -\eta \eta }$ and $\mathrm{\pi K-\eta K})$, for the first time, the existence of the scalar $\mathrm{\sigma (600)}$ and $\mathrm{\kappa (700)}$ mesons are confirmed in one-meson-exchange model. There are two kinds of form factors in our model: the monopole and the Gaussian. Our recent results show that the poles $\sigma $ and $\kappa $ appear at around $\mathrm{410-i540}$MeV and $\mathrm{650-i20}$MeV for monopole form factors, respectively. For Gaussian form factors, the poles $\sigma $ and $\kappa $, respectively, are at $\mathrm{360-i510}$MeV and $\mathrm{649-i190}$MeV.