New data on theKK¯threshold region and the nature of thef0(S*)

We combine new data on $f_0\left(S^{*}\right)$ production in $\frac{J}{\psi }$ and $D_s$ decays with earlier information on central production and elastic $\pi \pi$, $K\overline{K}$ processes to make a fresh examination of the $f_0\left(S^{*}\right)$ resonance. The key feature of our amplitude analysis is its strict enforcement of unitarity. This allows the good energy resolution of the new $\frac{J}{\psi }\to \phi \pi \pi \left(K\overline{K}\right)$ data to play its full role in delineating the $f_0\left(S^{*}\right)$ resonance structure that experiment demands. This enables us to distinguish alternative resonance mechanisms that have been proposed: we conclude that $f_0\left(S^{*}\right)$ is most probably not a $K\overline{K}$ molecule, nor an amalgam of two resonances, but a conventional Breit-Wigner-like structure. In this preferred description, the $f_0\left(S^{*}\right)$ has rather a narrow width (${\Gamma }_0\sim 52$ MeV) and comparable couplings to $\pi \pi$ and $K\overline{K}$. Possible spectroscopic interpretations are considered.