The role of $f_0(1710)$ in the $\phi \omega$ threshold peak of $J/\Psi \to \gamma \phi \omega$

TL;DR

This paper investigates the peak near the $ ext{phi} ext{omega}$ threshold in $J/ ext{Psi} o ext{gamma} ext{phi} ext{omega}$ decays, attributing it to the dynamical generation of the $f_0(1710)$ resonance rather than a new particle.

Contribution

The study demonstrates that the $ ext{phi} ext{omega}$ peak arises from vector-vector interactions generating the $f_0(1710)$, clarifying its nature and explaining experimental observations.

Findings

The peak is not due to a new resonance but to the $f_0(1710)$ generated dynamically.

The shape and strength of the $ ext{phi} ext{omega}$ distribution are explained by the vector-vector interaction mechanism.

The absence of a peak in $K ar K$ spectrum supports the dynamical generation interpretation.

Abstract

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