Exploring fully heavy scalar tetraquarks $QQ\overline{Q}\overline{Q}$

The masses, current couplings and widths of the fully heavy scalar tetraquarks $X_{\mathrm{4Q}}=QQ\overline{Q}\overline{Q}$, $Q=c, b$ are calculated by modeling them as four-quark systems composed of axial-vector diquark and antidiquark. The masses $m^{(\prime)}$ and couplings $f^{(\prime)}$ 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 $\langle \alpha _{s}G^{2}/ \pi \rangle$. Results $m=(6570 \pm 55)~\mathrm{MeV}$ and $m^{\prime}=(18540 \pm 50)~\mathrm{MeV}$ are used to fix kinematically allowed hidden-flavor decay channels of these states. It turns out that, the processes $X_{\mathrm{4c}}\rightarrow J/\psi J/\psi$, $X_{\mathrm{4c}}\rightarrow \eta _{c}\eta _{c}$, and $X_{\mathrm{4c }}\rightarrow \eta _{c}\chi _{c1}(1P)$ are possible decay modes of $X_{ \mathrm{4c}}$. 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 $X_{\mathrm{4c}}$ and mesons at relevant vertices. The couplings $g_{i}$ are extracted from the QCD three-point sum rules by extrapolating corresponding form factors $g_{i}(Q^2)$ to the mass-shell of a final meson. The mass of the scalar tetraquark $X_{\mathrm{4b}}$ is below the $\eta_b \eta_b$ and $\Upsilon(1S)\Upsilon(1S)$ thresholds, therefore it does not fall apart to these bottomonia, but transforms to conventional particles through other mechanisms. Comparing $m=(6570 \pm 55)~\mathrm{MeV}$ and $\Gamma _{\mathrm{4c}}=(110 \pm 21)~\mathrm{MeV}$ with parameters of structures observed by the LHCb, ATLAS and CMS collaborations, we interpret $X_{4c}$ as the resonance $X(6600)$ reported by CMS. Comparisons are made with other theoretical predictions.