We have recently completed the coupled dispersive analysis of  pi pi -> K anti-K We show that just fitting data fails to satisfy the dispersive representation and leads to inconsistencies with threshold sum-rules as well as unreliable resonance parameterizations. Our main result is a set of constrained fits to data that satisfy 16 dispersion relations of different kinds and allow for a reliable extraction of threshold and subtreshold parameters to be compared with Chiral Perturbation Theory and lattice QCD. In addition, we obtain a precise dispersive determination of the controversial light kappa-meson parameters, which has therefore become a “confirmed” state in the PDG, completing the light meson scalar nonet. The constrained fits to data are easy to implement and ready for further theoretical and experimental studies.

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