Fully charmed resonance $X(6900)$ and its beauty counterpart

Abstract

The fully heavy scalar tetraquarks $T_{4Q}=QQ\overline{Q}\overline{Q}$, ($Q=c,b$) are explored in the context of QCD sum rule method. We model $T_{4Q}$ as diquark-antidiquark systems composed of pseudoscalar constituents, and calculate their masses $m^{(\prime )}$ and couplings $f^{(\prime )}$ within the two-point sum rule approach. Our results $m=(6928\pm 50)\mathrm{MeV}$ and $m^{\prime }=(18858\pm 50)\mathrm{MeV}$ for masses of the tetraquarks $T_{4c}$ and $T_{4b}$ prove that they can decay to hidden-flavor heavy mesons. The full width ${\Gamma }_{4c}$ of the $T_{4c}$ is evaluated by taking into account the decay channels $T_{4c}\to J/\psi J/\psi$, $J/\psi {\psi }^{\prime }$, ${\eta }_c{\eta }_c$, ${\eta }_c{\eta }_c(2S)$, ${\eta }_c{\chi }_{c1}(1P)$, and ${\chi }_{c0}{\chi }_{c0}$. The partial widths of these processes depend on strong couplings $g_i$ at vertices $T_{4c}J/\psi J/\psi$, $T_{4c}J/\psi {\psi }^{\prime }$ etc., which are computed using the QCD three-point sum rule method. The decay $T_{4b}\to {\eta }_b{\eta }_b$ is used to find the width ${\Gamma }_{4b}$ of the $T_{4b}$. The predictions for $m$ and ${\Gamma }_{4c}=(128\pm 22)\mathrm{MeV}$ are compared with parameters of the fully charmed resonances reported by the LHCb, ATLAS, and CMS Collaborations. Based on this analysis, we interpret the tetraquark $T_{4c}$ as a candidate to the resonance $X(6900)$. The mass $m^{\prime }$ and width ${\Gamma }_{4b}=(94\pm 28)\mathrm{MeV}$ of the exotic meson $T_{4b}$ can be used in future experimental investigations of these

Comments: 14 Pages, 6 Figures and 2 Tables. arXiv admin note: text overlap with arXiv:2304.03244