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

TL;DR

This paper advances the precision of QCD sum rule calculations for the kaon distribution amplitude by including NNLO radiative corrections, leading to a more accurate determination of the first Gegenbauer moment.

Contribution

It provides the first NNLO (O(αs^2)) calculation of gluon radiative corrections to the sum rule for the kaon distribution amplitude, with complete factorization and improved accuracy.

Findings

Calculated $a_1^K(1 ext{ GeV})=0.10\u00b10.04$ with radiative corrections.

Achieved NNLO accuracy for perturbative and condensate contributions.

Implemented complete factorization removing quark mass logarithms.

Abstract

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 $a_1^K(1 \GeV)=0.10\pm 0.04$.