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We calculate the two-point correlation function using the interpolatingcurrent with $J^{PC}=2^{-}$. After performing the Borel sum rule analysis, theextracted masses of the $2^{--}$ tensor charmonium and bottomonium are$3.97\pm0.25$ GeV and $10.13\pm0.34$ GeV respectively. For comparison, we alsoperform the moment sum rule analysis for the charmonium and bottomoniumsystems. We extend the same analysis to study the $\bar qq, \bar qs, \bar ss,\bar qc, \bar sc, \bar qb, \bar sb$ and $\bar cb$ systems. Their masses are$1.78\pm 0.12, 1.85\pm 0.14, 2.00\pm 0.16, 2.86\pm 0.14, 3.01\pm 0.21,5.66\pm0.33, 6.40\pm 0.25$, and $7.08\pm 0.34$ GeV respectively.

Masses of the tensor mesons with $J^{P}=2^{-}$