Abstract
A new dispersion relation for the partial wave ππ scattering S matrix is set up. Using the dispersion relation we generalize the single channel unitarity condition, SS +=1, to the entire complex s plane, which is equivalent to the generalized unitarity condition in quantum mechanics. The pole positions of the σ resonance and the f 0(980) resonance are estimated based on the theoretical relations we obtained. The central value of the σ pole position is M σ ≃410 MeV, Γ σ ≃550 MeV, obtained after including the constraint of the Adler zero condition.
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