Exploring fully heavy scalar tetraquarks

The masses, current couplings and widths of the fully heavy scalar tetraquarks ${X}_{4Q}=QQ\stackrel{‾}{Q}\stackrel{‾}{Q}$, $Q=c,b$ are calculated by modeling them as four-quark systems composed of axial-vector diquark and antidiquark. The masses ${m}^{\left(\prime \right)}$ and couplings ${f}^{\left(\prime \right)}$ of these tetraquarks are computed in the context of the QCD sum rule method by taking into account a nonperturbative term proportional to the gluon condensate $〈{\alpha }_{s}{G}^{2}/\pi 〉$. Results $m=\left(6570±55\right)\phantom{\rule{0.25em}{0ex}}\text{MeV}$ and ${m}^{\prime }=\left(18540±50\right)\phantom{\rule{0.25em}{0ex}}\text{MeV}$ are used to fix kinematically allowed hidden-flavor decay channels of these states. It turns out that, the processes ${X}_{4c}\to J/\psi J/\psi $, ${X}_{4c}\to {\eta }_{c}{\eta }_{c}$, and ${X}_{4c}\to {\eta }_{c}{\chi }_{c1}\left(1P\right)$ are possible decay modes of ${X}_{4c}$. The partial widths of these channels are evaluated by means of the couplings ${g}_{i},i=1,2,3$ which describe strong interactions of tetraquark ${X}_{4c}$ and mesons at relevant vertices. The couplings ${g}_{i}$ are extracted from the QCD three-point sum rules by extrapolating corresponding form factors ${g}_{i}\left({Q}^{2}\right)$ to the mass-shell of a final meson. The mass of the scalar tetraquark ${X}_{4b}$ is below the ${\eta }_{b}{\eta }_{b}$ and $\Upsilon \left(1S\right)\Upsilon \left(1S\right)$ thresholds, therefore it does not fall apart to these bottomonia, but transforms to conventional particles through other mechanisms. Comparing $m=\left(6570±55\right)\phantom{\rule{0.25em}{0ex}}\text{MeV}$ and ${\Gamma }_{4c}=\left(110±21\right)\phantom{\rule{0.25em}{0ex}}\text{MeV}$ with parameters of structures observed by the LHCb, ATLAS and CMS collaborations, we interpret ${X}_{4c}$ as the resonance $X\left(6600\right)$ reported by CMS. Comparisons are made with other theoretical predictions.