Application of hard-pion four-point functions to pion-pion scattering
Application of hard-pion four-point functions is made to ππ scattering on the basis of the SU(2)×SU(2) current algebra, a conserved vector current, a partially conserved axial-vector current, and the hypothesis of single-meson dominance of intermediate states in T products. The calculation uses techniques previously developed for exploiting the content of the current algebra and the subsidiary conditions for an N-point process. The ππ scattering amplitude is shown to include, besides the well-known pole diagrams, a set of seagull terms. The Weinberg scattering lengths and effective ranges are found to be accurate to within a few percent, since the hard-pion corrections at threshold are only of O(mπ2/mρ2). In the low-energy region, the scattering-phase shifts are seen to be generally small and essentially model-independent, while at the K-meson mass δ00-δ02≃35°. All existing data (up to 1 GeV) can be fitted by adjusting one model-dependent parameter
