  We applied QCD Light Cone Sum Rules to estimate power corrections to the
helicity-conserving amplitude in the process $\gamma^*\gamma\to \pi\pi$. We
found that above $Q^2 \sim 4$ GeV$^2$ power corrections are numerically small
and the twist-2 part dominates.The amplitude can be reliably calculated in this
region using models of $2 \pi$ distribution amplitudes as an input. We found
that the magnitude of the NLO corrections depends rather strongly on the
normalization of the gluonic distribution amplitude.
