A glueball puzzle explained in terms of $φh_1(1380)$ dynamics: Aka $X(2370)$

Abstract: We study the interaction of $φ$ with $h_1(1380)$, considering the latter as a $K^*\bar K$ molecular state, and find the generation of a state with the same quantum numbers, together with a mass and width compatible with the experimental results, as those of $X(2370)$, recently advocated as a candidate for a glueball. Within our description, the suppressed decay modes of $X(2370)$ to $γω$, $ωφ$ and $K^*\bar K$, reported in the experimental paper as clues to its glueball nature, are naturally explained. Conversely, the non $K^* \bar K$ decay to $K \bar K π$ (the latter being the invariant mass where the resonance is observed) is shown to be largely enhanced due to the combination of a triangle singularity and the presence of $K(1630)$ in the $ρφ\to \bar K$ vertex involved in the triangle loop.