The KK effect in ππ scattering

The current picture of s-wave isoscalar ππ scattering shows a sharp rise of the phase shift δ₀₀ through a resonance just below the $\text{K}\text{K}$ threshold. A model based on coupled ππ and $\text{K}\text{K}$ channels is developed for understanding this phenomenon. The method is one in which we analyze four form factors: the π to π and K to K matrix elements of two isoscalar sigma commutators derived from $\text{(3,}\text{3}\text{) + (}\text{3}\text{,3)}$ symmetry breaking. The equations for the system of coupled form factors are obtained from hard-meson current algebra and solved in terms of analytic functions having the ππ and $\text{K}\text{K}$ cuts. Unitarity is invoked to extract the desired ππ phase shift. The dramatic influence of the $\text{K}\text{K}$ channel is apparent in the solution and an excellent fit to the recent data is obtained. An S¹ resonance is among the resutls; the resonance pole on the second sheet is found at complex energy $\text{M ?}\text{1}\text{2}\text{iΓ = (1006?23i)}\text{MeV}$.