Pion-pion scattering amplitude. II. Improved analysis aboveK¯Kthreshold

We improve, in the energy region between $\bar{K}K$ threshold and $\sim~1.4$GeV, the energy-dependent phase shift analysis of $\pi\pi$ scattering presentedin a previous paper. For the S0 wave we have included more data above$\bar{K}K$ threshold and we have taken into account systematically theelasticity data on the reaction $\pi\pi\to\bar{K}K$. We here made a coupledchannel fit. For the D0 wave we have considered information on low energyparameters, and imposed a better fit to the $f_2$ resonance. For both waves theexpressions we now find are substantially more precise than the previous ones.We also provide slightly improved D2 and P waves, including the estimatedinelasticity for the first, and a more flexible parametrization between 1 and1.42 GeV for the second. The accuracy of our amplitudes is now such that itrequires a refinement of the Regge analysis, for $s^{1/2}\geq1.42$ GeV, whichwe also carry out. We show that this more realistic input produces $\pi\pi$scattering amplitudes that satisfy better forward dispersion relations,particularly for $\pi^0\pi^0$ scattering.Comment: Plain TeX. 12 figures. Minor anomaly in the K-matrix fit corrected by moving matching point to 932 MeV, and pole $M_1$ to 910.6 MeV. Results unaltere