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We improve our description of pion-pion scattering data by imposingadditional requirements to our previous fits, in the form of once-subtractedRoy-like equations, while extending our analysis up to 1100 MeV. We providesimple and ready to use parametrizations of the amplitude. In addition, wepresent a detailed description and derivation of these once-subtracteddispersion relations that, in the 450 to 1100 MeV region, provide an additionalconstraint which is much stronger than our previous requirements of ForwardDispersion Relations and standard Roy equations. The ensuing constrainedamplitudes describe the existing data with rather small uncertainties in thewhole region from threshold up to 1100 MeV, while satisfying very stringentdispersive constraints. For the S0 wave, this requires an improved matching ofthe low and high energy parametrizations. Also for this wave we have consideredthe latest low energy Kl4 decay results, including their isospin violationcorrection, and we have removed some controversial data points. These changeson the data translate into better determinations of threshold and subthresholdparameters which remove almost all disagreement with previous ChiralPerturbation Theory and Roy equation calculations below 800 MeV. Finally, ourresults favor the dip structure of the S0 inelasticity around the controversial1000 MeV region.

The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV