H.Q. Zheng

The constraints of unitary on ππ scattering dispersion relations

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 ≃410xa0MeV, Γ σ ≃550xa0MeV, obtained after including the constraint of the Adler zero condition.

The [1, 2] Padé amplitudes for ππ scatterings in chiral perturbation theory

Abstract A detailed analysis to the [1,2] Pade approximation to the ππ scattering 2-loop amplitudes in chiral perturbation theory is made.