Pion-pion scattering amplitude. II. Improved analysis above K̅K threshold

We improve, in the energy region between the K̅K threshold and ~ 1.4 GeV, the energy-dependent phase shift analysis of π π scattering presented in a previous paper. For the S0 wave, we have included more data above the K̅K threshold and we have taken into account systematically the elasticity data on the reaction π π →K̅K. We here made a coupled channel fit. For the D0 wave, we have considered information on low energy parameters, and imposed a better fit to the f_2 resonance. For both waves the expressions we now find are substantially more precise than the previous ones. We also provide slightly improved D2 and P waves, including the estimated inelasticity for the first, and a more flexible parametrization between 1 and 1.42 GeV for the second. The accuracy of our amplitudes is now such that it requires a refinement of the Regge analysis, for^(1/2) ≥ 1.42 GeV, which we also carry out. We show that this more realistic input produces π π scattering amplitudes that satisfy better forward dispersion relations, particularly for π^0 π^0 scattering