Forward dispersion relations and Roy equations in <Emphasis Type="Italic">ππ</Emphasis> scattering

We first review the results of an analysis of ππ interactions in S, P and D waves for the two-pion effective mass from threshold to about 1.4GeV. In particular, we show a recent improvement of this analysis above the Kˉ threshold using more data for phase shifts and including the S0-wave inelasticity from ππ→Kˉ. In addition, we have improved the fit to the f ₂(1270)-resonance and used a more flexible P-wave parametrization above the Kˉ threshold and included an estimation of the D2-wave inelasticity. The better accuracy thus achieved also required a refinement of the Regge analysis above 1.42GeV. Finally, in this work we check that the ππ scattering amplitudes obtained in this approach satisfy remarkably well forward dispersion relations and Roy's equations.