$\pi \pi$ Invariant mass spectrum in $V^{\mathrm{\prime }}\to V\pi \pi$ and the $f_0(600)$ pole

We consider the phenomenological description of the two pion invariant mass spectrum in the $V^{\mathrm{\prime }}\to V\pi \pi$ 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 $\mathrm{{\rm Y}}(nS)$ and $\mathrm{\Psi }(nS)$ we determine the $f_0(600)$ mass and width to be $m_{f_0}=528\pm 32$ MeV and ${\mathrm{\Gamma }}_{f_0}=413\pm 45$ MeV. The mass and width values we report correspond to the real and imaginary part of the S matrix pole respectively.