Improving $\pi\pi$ dispersive analyses and resonance determination with Forward Dispersion Relations

TL;DR

This paper advances pion-pion scattering analysis by refining inelasticity treatment, extending dispersion relations, and extracting resonance parameters in a model-independent manner, leading to more reliable resonance solutions.

Contribution

It introduces improved dispersive analysis techniques including G-waves and extended constraints, enhancing resonance determination in pion-pion scattering.

Findings

Three reliable solutions for different datasets.

Resonance pole parameters extracted independently of models.

Extended dispersion relations up to 1.6 GeV.

Abstract

We present preliminary results of an improved pion-pion scattering dispersive analysis that includes: a refined treatment of inelasticities, the introduction of G-waves, the extension of Forward Dispersion Relations as constraints up to 1.6 GeV, and data description up to roughly 1.8 GeV. Additionally, we impose Roy-like dispersion relations. As a result, we obtain three reliable solutions corresponding to three different datasets. From the Forward Dispersion Relation output, we extract resonance pole parameters in a parameterization-independent way using continued fractions.