Forward dispersion relations and Roy equations in pi-pi scattering

We review results of an analysis of pipi interactions in S, P and D waves for two-pion effective mass from threshold to about 1.4 GeV. In particular we show a recent improvement of this analysis above the K anti-K threshold using more data for phase shifts and including the S0 wave inelasticity from pipi -> K anti-K. In addition, we have improved the fit to the f2(1270) resonance and used a more flexible P wave parametrization above the K anti-K threshold and included an estimation of the D2 wave inelasticity. The better accuracy thus achieved also required a refinement of the Regge analysis above 1.42 GeV. We have checked that the pipi scattering amplitudes obtained in this approach satisfy remarkably well forward dispersion relations and Roy's equations.Comment: 6 pages, invited talk to the IV International Conference on Quarks and Nuclear Physics QNP06, Madrid 5th-10th June 200