A glueball puzzle explained in terms of $\varphi h_1(1380)$ dynamics: Aka $X(2370)$

Abstract

We study the interaction of $\varphi$ with $h_1(1380)$, considering the latter as a $K^{\ast }\bar{K}$ 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 $\gamma \omega$, $\omega \varphi$ and $K^{\ast }\bar{K}$, reported in the experimental paper as clues to its glueball nature, are naturally explained. Conversely, the non $K^{\ast }\bar{K}$ decay to $K\bar{K}\pi$ (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 $\rho \varphi \to \bar{K}$ vertex involved in the triangle loop.