The mass and width of the tensor tetraquark.. =........ with spin-parity.. P = 2+ are calculated in the context of the QCD sum rule method. The tetraquark.. is modeled as a diquark-antidiquark state built of components............ and............ with.. being the charge conjugation matrix. The mass.. = (12.795 +/- 0.095) GeV of the exotic tensor meson.. is found by means of the two-point sum rule approach. Its full width G is evaluated by considering processes..... ....-..,..-....*-.., and..*-....*-... Partial widths of these decays are computed by means of the threepoint sum rule approach which is used to determine the strong couplings at relevant tetraquark-meson-meson vertices. Predictions obtained for the width GT = 55.5+10.6 -9.9 MeV, as well as the mass of the tetraquark.. can be useful in investigations of fully heavy four-quark mesons.Iran National Science Foundation (INSF) [4025036]K. Azizi is thankful to Iran National Science Foundation (INSF) for the partial financial support provided under the elites Grant No. 4025036
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