Understanding the $0^{++}$ and $2^{++}$ charmonium(-like) states near 3.9 GeV

TL;DR

This paper analyzes experimental data on certain charmonium-like states near 3.9 GeV, proposing they are related molecular states and clarifying their nature through coupled-channel dynamics, which enhances understanding of charmonium spectrum and hadron interactions.

Contribution

The study introduces a coupled-channel analysis that unifies various experimental observations, identifying multiple hidden-charm molecular states and clarifying the nature of the $X(3915)$ and $X(3960)$.

Findings

Identification of four hidden-charm scalar molecular states around 3.73, 3.94, 3.99, and 4.23 GeV.

Reproduction of experimental data across different processes with coupled-channel dynamics.

Clarification of the relationship between $X(3915)$, $X(3960)$, and charmonium states.

Abstract

We propose that the $X(3915)$ observed in the $J/\psi\,\omega$ channel is the same state as the $\chi_{c2}(3930)$, and the $X(3960)$, observed in the $D_s^+D_s^-$ channel, is an $S$-wave $D_s^+ D_s^-$ hadronic molecule. In addition, the $J^{PC}=0^{++}$ {component in the $B^+\to D^+D^-K^+$} assigned to the $X(3915)$ in the current {\it Review of Particle Physics} has the same origin as the $X(3960)$, which has a mass around 3.94~GeV. To check the proposal, the available data in the $D\bar D$ and $D_s^+ D_s^-$ channels from both $ B$ decays and $\gamma\gamma$ fusion reaction are analyzed considering both the $D\bar D$-$D_s\bar D_s$-$D^*\bar D^*$-$D_s^*\bar D_s^*$ coupled channels with $0^{++}$ and a $2^{++}$ state introduced additionally. It is found that all the data in different processes can be simultaneously well reproduced, and the coupled-channel dynamics produce four hidden-charm scalar molecular states with masses around 3.73, 3.94, 3.99 and 4.23~GeV, respectively. The results may deepen our understanding of the spectrum of charmonia as well as of the interactions between charmed hadrons.