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

TL;DR

This paper refines pion-pion scattering amplitude analysis up to 1100 MeV by implementing once-subtracted Roy-like equations, resulting in more accurate, constrained amplitudes that align well with theoretical predictions and experimental data.

Contribution

It introduces a novel application of once-subtracted Roy-like equations extending the energy range and improves data fits with tighter dispersive constraints and updated low-energy inputs.

Findings

Enhanced amplitude parametrizations with smaller uncertainties.

Better agreement with Chiral Perturbation Theory below 800 MeV.

Support for the dip structure in S0 inelasticity around 1000 MeV.

Abstract

We improve our description of pion-pion scattering data by imposing additional requirements to our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of Forward Dispersion Relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy Kl4 decay results, including their isospin violation correction, and we have removed some controversial data points. These changes on the data translate into better determinations of threshold and subthreshold parameters which remove almost all disagreement with previous Chiral Perturbation Theory and Roy equation calculations below 800 MeV. Finally, our results favor the dip structure of the S0 inelasticity around the controversial 1000 MeV region.