Hadronic molecules ${\eta }_c{\eta }_c$ and ${\chi }_{c0}{\chi }_{c0}$

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 $m$, $\tilde{m}$ and current couplings $f$, $\tilde{f}$ of these states are calculated using the two-point sum rule approach. The obtained results $m=(6264\pm 50)\mathrm{MeV}$ and $\tilde{m}=(6954\pm 50)\mathrm{MeV}$ 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 ${\mathcal{M}}_{1}J/\psi J/\psi$, ${\mathcal{M}}_1{\eta }_c{\eta }_c$, 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.

Comments: 16 Pages, 4 Figures and 2 Tables. arXiv admin note: text overlap with arXiv:2304.03244, arXiv:2304.09943