Precise analysis of pion-pion scattering data from Roy equations and forward dispersion relations

TL;DR

This paper presents a precise, model-independent analysis of pion-pion scattering data using Roy equations and forward dispersion relations, improving the understanding of low-energy hadronic interactions.

Contribution

It introduces a new set of once-subtracted coupled equations for partial waves and compares unconstrained and dispersion-constrained fits for pion-pion scattering.

Findings

Dispersive analysis yields highly precise data descriptions

Independent fits satisfy dispersive representations well

Constrained fits enhance data consistency and accuracy

Abstract

We review our recent analysis of pion-pion scattering data in terms of Roy equations and Forward Dispersion Relations, and present some preliminary results in terms of a new set of once-subtracted coupled equations for partial waves. The first analysis consists of independent fits to the different pion-pion channels that satisfies rather well the dispersive representation. In the second analysis we constrain the fit with the dispersion relations. The latter provides a very precise and model independent description of data using just analyticity, causality and crossing.