On the determination of $\sigma$ from experimental data on the $\pi\pi$ isoscalar $S$-wave at low energies

TL;DR

This paper analyzes low-energy $11$ scattering data, including recent precise measurements, to determine the $1$ pole, providing results consistent with chiral perturbation theory but with larger uncertainties.

Contribution

It introduces a comprehensive analysis of $11$ scattering data using conformal expansions, incorporating new experimental data to refine the $1$ pole determination.

Findings

Consistent $1$ mass and width with recent ChPT and Roy equation results.

Larger theoretical uncertainties compared to previous methods.

Inclusion of recent $K_{e4}$ decay data improves analysis robustness.

Abstract

We investigate the determination of the pole associated to $\sigma$ from $\pi\pi$ scattering data below the $K\bar{K}$ threshold, including the new precise data from $K_{e4}$ decay reported recently by the NA48/2 Collaboration. Using a large class of analytic parametrizations based on expansions in powers of conformal variables, we obtain for the mass and width of $\sigma$ values which are consistent with those calculated recently using ChPT and Roy equations, but have larger theoretical uncertainties.