Forward dispersion relations and Roy equations in π π scattering

We first review the results of an analysis of π π 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 KK̅ threshold using more data for phase shifts and including the S0-wave inelasticity from π π-> KK̅ . In addition, we have improved the fit to the f_(2)(1270)resonance and used a more flexible P-wave parametrization above the KK̅ threshold and included an estimation of the D_2 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 pi pi scattering amplitudes obtained in this approach satisfy remarkably well forward dispersion relations and Roy's equations