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

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