# Global parameterization of $\pi \pi$ scattering up to 2 GeV

## TL;DR

This paper provides comprehensive parameterizations of $$ scattering partial waves up to 2 GeV, integrating previous dispersive analyses and experimental data to accurately describe resonance poles and scattering behavior.

## Contribution

It offers the first global parameterizations of $$ scattering up to 2 GeV that incorporate dispersive analyses, uncertainties, and experimental data in a unified framework.

## Key findings

- Accurately describes $$ scattering up to 2 GeV.
- Reproduces dispersive determinations of key resonance poles.
- Provides parameterizations consistent with dispersion relations.

## Abstract

We provide global parameterizations of $\pi\pi$ scattering $S0$ and $P$ partial waves up to roughly 2 GeV for phenomenological use. These parameterizations describe the output and uncertainties of previous partial-wave dispersive analyses of $\pi\pi$, both in the real axis up to 1.12 GeV and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.43 GeV. Above that energy we just describe the available experimental data. Moreover, the analytic continuations of these global parameterizations also describe accurately the dispersive determinations of the $\sigma/f_0(500)$, $f_0(980)$ and $\rho(770)$ pole parameters.