Form factors of D decays into JPC=2++ tensor mesons are calculated in the light-cone sum rules approach up to twist-4 distribution amplitudes of the tensor meson. The masses of the tensor mesons are comparable to that of the charm quark mass mc
Nearby in the stack
; therefore all terms including powers of
mT/mc
are kept out in the expansion of the two-particle distribution amplitude
⟨T∣qˉ1α(x)q2δ(0)∣0⟩
. Branching ratios of the semileptonic
D→Tμνˉμ
decays and nonleptonic
D→TP(P=K,π)
decays are taken into consideration. A comparison is also made between our results and predictions of other methods and the existing experimental values for the nonleptonic case. The semileptonic branching ratios are typically of the order of
10−5
, and the nonleptonic ones show better agreement with the experimental data in comparison to the Isgur-Scora-Grinstein-Wise predictions.