Pion scalar form factor and model independent values of $f_0(500)$ and $f_0(980)$ meson parameters

Abstract

The pion scalar form factor along with all existing S-wave iso-scalar $\pi\pi$-scattering phase shift data in the elastic region up to $1 {\rm GeV}^2$ are applied for a determination of the $f_0(500)$ and $f_0(980)$ meson parameters $m_{f_0(500)}=(360\pm33){\rm MeV}$, $\Gamma_{f_0(500)}=(587\pm 85){\rm MeV}$ and $m_{f_0(980)}=(957\pm77) {\rm MeV}$, $\Gamma_{f_0(980)}=(164\pm142){\rm MeV}$ in a model independent way.