The role of $f_0(1710)$ in the $\varphi \omega$ threshold peak of $J\mathrm{/}\mathrm{\Psi }\to \gamma \varphi \omega$

We study the process $J\mathrm{/}\mathrm{\Psi }\to \gamma \varphi \omega$, measured by the BES experiment, where a neat peak close to the $\varphi \omega$ threshold is observed and is associated to a scalar meson resonance around 1800 MeV. We make the observation that a scalar resonance coupling to $\varphi \omega$ unavoidably couples strongly to $K\bar{K}$, but no trace of a peak is seen in the $K \bar K$spectrumofthe$J/\Psi \to \gamma K \bar K$ at this energy. This serves us to rule out the interpretation of the observed peak as a signal of a new resonance. After this is done, a thorough study is performed on the production of a pair of vector mesons and how its interaction leads necessarily to a peak in the $J\mathrm{/}\mathrm{\Psi }\to \gamma \varphi \omega$ reaction close to the $\varphi \omega$ threshold, due to the dynamical generation of the $f_0(1710)$ resonance by the vector-vector interaction. We then show that both the shape obtained for the $\varphi \omega$ mass distribution, as well as the strength are naturally reproduced by this mechanism. The work also explains why the $\varphi \omega$ peak is observed in the BES experiment and not in other reactions, like $B^\pm\to K^\pm \phi\omega$ of Belle.