$ππ$ Invariant mass spectrum in $V'\to V~ππ$ and the $f_0(600)$ pole

Abstract

We consider the phenomenological description of the two pion invariant mass spectrum in the $V' \to V ππ$ decays. We study the parametrization of the amplitude involving both $S$ and $D$ wave contributions. From a fit to the two pion decays of the $ Υ(nS)$ and $Ψ(nS)$ we determine the $f_0 (600)$ mass and width to be $m_{f_0}=528 \pm 32$ MeV and $Γ_{f_0}=413\pm 45$ MeV. The mass and width values we report correspond to the real and imaginary part of the S matrix pole respectively.