Hadronic molecules $\eta_c \eta_c$ and $\chi_{c0}\chi_{c0}$

TL;DR

This paper investigates fully charmed scalar hadronic molecules using QCD sum rules, calculating their masses, decay channels, and widths, and compares these with known resonances to identify potential candidates.

Contribution

It provides the first detailed QCD sum rule analysis of the $ ext{eta}_c ext{eta}_c$ and $ ext{chi}_{c0} ext{chi}_{c0}$ molecules, including mass, decay channels, and width estimations.

Findings

Mass of $ ext{eta}_c ext{eta}_c$ molecule: 6264 MeV

Mass of $ ext{chi}_{c0} ext{chi}_{c0}$ molecule: 6954 MeV

Estimated widths: 320 MeV and 138 MeV

Abstract

The fully charmed hadronic scalar molecules $\mathcal{M}_1=\eta_c \eta_c$ and $\mathcal{M}_2=\chi_{c0}\chi_{c0}$ are studied in the context of the QCD sum rule method. The masses $m$, $\widetilde{m}$ and current couplings $f$, $ \widetilde{f}$ of these states are calculated using the two-point sum rule approach. The obtained results $m=(6264 \pm 50)~\mathrm{MeV}$ and $ \widetilde{m}=(6954 \pm 50)~\mathrm{MeV}$ are employed to determine their decay channels. It is demonstrated that the processes $\mathcal{M}_1\to J/\psi J/\psi $ and $\mathcal{M}_1\to \eta _{c}\eta _{c}$ are kinematically allowed decay modes of $\mathcal{M}_1$. The molecule $\mathcal{M}_2$ decays to $J/\psi J/\psi$, $J/\psi \psi^{\prime}$, $\eta _{c}\eta _{c}$, $\eta _{c}\eta _{c}(2S)$, $\eta _{c}\chi _{c1}(1P)$, and $\chi_{c0} \chi_{c0}$ mesons. The partial widths all of these processes are evaluated by means of the three-point sum rule calculations, which are necessary to extract the strong couplings $g_i$ at vertices $\mathcal{M}_1J/\psi J/\psi $, $\mathcal{M }_1\eta _{c}\eta _{c}$, and others. Our estimates for the full widths of the molecules $\Gamma_{\mathcal{M}_1}=(320 \pm 72)~\mathrm{MeV}$ and $\Gamma _{ \mathcal{M}_2}=(138 \pm 18)~\mathrm{MeV}$, as well as their masses are compared with parameters of the $X$ resonances discovered by the LHCb-ATLAS-CMS Collaborations in the di-$J/\psi$ and $J/\psi\psi^{\prime}$ invariant mass distributions. We argue that the molecule $\mathcal{M}_1$ can be considered as a real candidate to the resonance $X(6200)$. The structure $ \mathcal{M}_2$ may be interpreted as $X(6900)$ or one of its components in combination with a scalar tetraquark.