Theory of low-energy ππ scattering

A four-parameter family of solutions to the ππ partial-wave dispersion relations is obtained using the inverse amplitude method. Choosing the parameters consistent with phenomenological values and so as to maximize agreement with rigorous sum rules and inequalities leads to a firm prediction of the phase shifts for S and P wave scattering and for the amplitudes below threshold. Neglecting inelasticity, the I = 0S-wave resonates near $\text{s}\text{= 540}\text{MeV}$, the I = 2 S-wave falls to about ?12° near 1 GeV, and the P-wave is ?-dominated. The S-waves have subthreshold zeroes consistent with the Adler condition. Inelastic effects are estimated and found to be small below the rho meson mass.