In this article, we calculate the contributions of the vacuum condensates up to dimension-6 in the operator product expansion and study the masses and decay constants of the heavy tensor mesons D_2~*(2460), D_(s2)~*(2573), B_2~* (5747), B_(s2)~*(5840) using the QCD sum rules. The predicted masses are in excellent agreement with the experimental data, while the ratios of the decay constants (~(fD_(s2)~*)/(~fD_2~*) ≈ (~fB_(s2)~*)/(~fB_2~*) ≈ (~fD_s)/(~fD) |_(exp), where the exp denotes the experimental value.
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