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The masses, current couplings and widths of the fully heavy scalartetraquarks $X_{\mathrm{4Q}}=QQ\overline{Q}\overline{Q}$, $Q=c, b$ arecalculated by modeling them as four-quark systems composed of axial-vectordiquark and antidiquark. The masses $m^{(\prime)}$ and couplings $f^{(\prime)}$ of these tetraquarks are computed in the context of the QCD sumrule method by taking into account a nonperturbative term proportional to thegluon condensate $\langle \alpha _{s}G^{2}/ \pi \rangle$. Results $ m=(6570 \pm55)~\mathrm{MeV}$ and $m^{\prime}=(18540 \pm 50)~\mathrm{MeV}$ are used to fixkinematically allowed hidden-flavor decay channels of these states. It turnsout 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 ofthe 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}$ areextracted from the QCD three-point sum rules by extrapolating correspondingform factors $g_{i}(Q^2) $ to the mass-shell of a final meson. The mass of thescalar tetraquark $X_{\mathrm{4b}}$ is below the $\eta_b \eta_b$ and$\Upsilon(1S)\Upsilon(1S)$ thresholds, therefore it does not fall apart tothese bottomonia, but transforms to conventional particles through othermechanisms. Comparing $m=(6570 \pm 55)~\mathrm{MeV}$ and $ \Gamma_{\mathrm{4c}}=(110 \pm 21)~\mathrm{MeV}$ with parameters of structuresobserved by the LHCb, ATLAS and CMS collaborations, we interpret $ X_{4c}$ asthe resonance $X(6600)$ reported by CMS. Comparisons are made with othertheoretical predictions.

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