Consistency checks of different pion-pion scattering data sets using forward dispersion relations

We review our evaluation of forward dispersion relations for direct fits to the different, and often conflicting, pion-pion scattering experimental analyses. We find that some of the most commonly used data sets do not satisfy these constraints by several standard deviations. We also provide a consistent pion-pion amplitude by improving a global fit to data with these dispersion relations.