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We calculate the $O(\alpha_s)$ and $O(\alpha_s^2)$ gluon radiativecorrections to the QCD sum rule for the first Gegenbauer moment $a_1^K$ of thekaon light-cone distribution amplitude. The NNL0 accuracy is achieved for theperturbative term and quark-condensate contributions to the sum rule. Acomplete factorization is implemented, removing logarithms of $s$-quark massfrom the coefficients in the operator-product expansion. The sum rule withradiative corrections yields $a_1^K(1 \GeV)=0.10\pm 0.04$.

Towards NNLO Accuracy in the QCD Sum Rule for the Kaon Distribution Amplitude