Meson-meson interactions in a nonperturbative chiral approach

A nonperturbative method which combines constraints from chiral symmetry breaking and coupled channel unitarity is used to describe the meson-meson interaction up to about 1.2 GeV. The approach uses the $\mathcal{O}{(p}^2)$ and $\mathcal{O}{(p}^4)$ chiral Lagrangians. The seven free parameters of the $\mathcal{O}{(p}^4)$ Lagrangian are fitted to the data. The results are in good agreement with a vast amount of experimental analyses. The amplitudes develop poles in the complex plane corresponding to the $f_0,\hspace{0.5em}{a}_0,\hspace{0.5em}\rho ,\hspace{0.5em}{K}^{*},\hspace{0.5em}\phi ,\hspace{0.5em}\sigma ,$ and $\kappa$ resonances, the latter two being very broad. The total and partial decay widths of the resonances are also well reproduced. Further extensions and applications of this chiral nonperturbative scheme are also discussed.