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In this article, we study the $J^{PC}=0^{++}$ and $2^{++}$ $QQ\bar{Q}\bar{Q}$ tetraquark states with the QCD sum rules, and obtain the predictions $M_{X(cc\bar{c}\bar{c},0^{++})} =5.99\pm0.08\,\rm{GeV}$, $M_{X(cc\bar{c}\bar{c},2^{++})} =6.09\pm0.08\,\rm{GeV}$, $M_{X(bb\bar{b}\bar{b},0^{++})} =18.84\pm0.09\,\rm{GeV}$ and $M_{X(bb\bar{b}\bar{b},2^{++})}=18.85\pm0.09\,\rm{GeV}$, which can be confronted to the experimental data in the future.
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