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

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.