Chiral-dispersive calculations of ππ scattering confront experiment

In a series of papers we have applied several sum rules and forward dispersion relations, to ππ scattering. We have found that some widely used data sets fail to satisfy these constraints, and we have provided an amplitude that describes data consistently with the dispersive tests. Furthermore, we noted that the input and precision claimed in a Roy equation analysis by Colangelo, Gasser and Leutwyler (CGL), lead to several mismatches with some sum rules. Subsequently, Caprini, Colangelo, Gasser and Leutwyler claimed that our Regge parametrization was incorrect. We collect here the answers to their various claims, and try to clarify the points of agreement and disagreement, showing experimental evidence that substantiates our results, and that, in addition, their representation fails to satisfy all three forward dispersion relations up to by several standard deviations.