Fully charmed resonance X(6900) and its beauty counterpart

Abstract

The fully heavy scalar tetraquarks $T_{\mathrm{4Q}}=QQ\bar{Q}\bar{Q}$, ($Q=c,b$) are explored in the context of QCD sum rule method. We model $T_{\mathrm{4Q}}$ 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 $T_{\mathrm{4c}}$ and $T_{\mathrm{4b}}$ prove that they can decay to hidden-flavor heavy mesons. The full width ${\Gamma }_{\mathrm{4c}}$ of the $T_{\mathrm{4c}}$ is evaluated by taking into account the decay channels $T_{\mathrm{4c}}\to J/\psi J/\psi$, $J/\psi {\psi }^{\prime }$, ${\eta }_c{\eta }_c$, ${\eta }_c{\eta }_c\left(2S\right)$, ${\eta }_c{\chi }_{c1}\left(1P\right)$, and ${\chi }_{c0}{\chi }_{c0}$. The partial widths of these processes depend on strong couplings $g_i$ at vertices $T_{\mathrm{4c}}J/\psi J/\psi$, $T_{\mathrm{4c}}J/\psi {\psi }^{\prime }$ etc., which are computed using the QCD three-point sum rule method. The decay $T_{\mathrm{4b}}\to {\eta }_b{\eta }_b$ is used to find the width ${\Gamma }_{\mathrm{4b}}$ of the $T_{\mathrm{4b}}$. The predictions for m and ${\Gamma }_{\mathrm{4c}}=(128\pm 22)\mathrm{MeV}$ 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 $T_{\mathrm{4c}}$ as a candidate to the resonance $X\left(6900\right)$. The mass $m^{\prime }$ and width ${\Gamma }_{\mathrm{4b}}=(94\pm 28)\mathrm{MeV}$ of the exotic meson $T_{\mathrm{4b}}$ can be used in future experimental investigations of these states.