Essentials of the σ resonance in meson-meson scattering and spectral functions

We study the roles of resonances in semi-local duality from meson-meson scattering and in the scalar and pseudoscalar spectral function sum rules. The scattering amplitudes and spectral functions are first systematically calculated within chiral perturbation theory (χPT) with explicit η1 field in addition to the pseudo-Goldstone octet π,K,η8 and then unitarized through the N/D approach. In this note, we emphasize the important roles of the σ or f0(500) resonance in these quantities.