The constraints of unitary on ππ scattering dispersion relations

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 f0(980) resonance are estimated based on the theoretical relations we obtained. The central value of the σ pole position is Mσ≃410 MeV, Γσ≃550 MeV, obtained after including the constraint of the Adler zero condition.