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

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