Molecular components in the $J/\psi$ and the $\rho$-$\pi$ puzzle

TL;DR

This paper proposes that certain molecular states involving $f_0(1710)$, $ ho$, and $\\pi$ particles can explain observed decay patterns of $J/\psi$ and shed light on the long-standing $\rho-\pi$ puzzle.

Contribution

It introduces a molecular scenario for $J/\psi$ decays, suggesting molecular components significantly influence decay channels and may resolve the $\rho-\pi$ puzzle.

Findings

Identification of molecular states $f_0(1710) \\omega$ and $f_0(1710) \\phi$ as $X(2440)$ and $X(2680)

Estimated branching fractions of these states in various decay channels

Large molecular components in $J/\psi$ affecting its decay behavior

Abstract

Motivated by the large branching fractions of $J/\psi \to f_0 (1710) \omega/f_0(1710) \phi$ and the light exotic candidates, we find that there may exist molecular states composed of $f_0(1710) \omega$ and $f_0 (1710) \phi$, which correspond to $X(2440)$ and $X(2680)$ observed in a few decades before. The branching fraction of $X(2440)$ and $X(2680)$ to various $PV$ channels and $KK\omega(\phi)$ channels are estimated in the molecular scenario. In addition, the large branching fractions of $J/\psi \to f_0 (1710) \omega/f_0(1710) \phi$ indicate the sizable molecular components in the $J/\psi$ state. Thus, we consider the $J/\psi$ as the supperposition of $c\bar{c}(1S)$, $f_0(1710) \omega$ and $f_0 (1710) \phi$ molecular states, and these molecular components have significant impact on the light hadron decays of $J/\psi$, which may shield light on the long standing $\rho-\pi$ puzzle.