The role of $f_0(1710)$ in the $ϕω$ threshold peak of $J/Ψ\to γϕω$

Abstract

We study the process $J/Ψ\to γϕω$, measured by the BES experiment, where a neat peak close to the $ϕω$ threshold is observed and is associated to a scalar meson resonance around 1800 MeV. We make the observation that a scalar resonance coupling to $ϕω$ unavoidably couples strongly to $K \bar K$, but no trace of a peak is seen in the $K \bar K$ spectrum of the $J/Ψ\to γK \bar K$ 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 $J/Ψ\to γϕω$ reaction close to the $ϕω$ 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 $ϕω$ mass distribution, as well as the strength are naturally reproduced by this mechanism. The work also explains why the $ϕω$ peak is observed in the BES experiment and not in other reactions, like $B^\pm\to K^\pm ϕω$ of Belle.