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We applied QCD Light Cone Sum Rules to estimate power corrections to thehelicity-conserving amplitude in the process $\gamma^*\gamma\to \pi\pi$. Wefound that above $Q^2 \sim 4$ GeV$^2$ power corrections are numerically smalland the twist-2 part dominates.The amplitude can be reliably calculated in thisregion using models of $2 \pi$ distribution amplitudes as an input. We foundthat the magnitude of the NLO corrections depends rather strongly on thenormalization of the gluonic distribution amplitude.Comment: 20 pages, 6 figure

Power corrections to the process $\gamma\gamma^*\rightarrow \pi\pi$ in the light-cone sum rules approach