We update the theoretical framework for the QCD calculation of transition form factors $gamma^*gammatoeta$ and $gamma^*gammatoeta$ at large photon virtualities including full next-to-leading order analysis of perturbative corrections, the charm quark contribution, and taking into account SU(3)-flavor breaking effects and the axial anomaly contributions to the power-suppressed twist-four distribution amplitudes. The numerical analysis of the existing experimental data is performed with these improvements.
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