  In the scaling regime, amplitudes for backward virtual Compton scattering and
hadron annihilation into two photons depend on structure functions that
describe the hadron-photon transition at the partonic level. We construct
simple analytical models for the vector and axial-vector pion-photon transition
distribution amplitudes based on double distributions. Via a sum rule, these
models are tuned to reproduce the pion-photon transition form factors. To
obtain reasonable estimates of the distributions at a low scale, we modify the
models to saturate the positivity bounds using empirically parametrized parton
distributions. We also determine a model-independent contribution to the
axial-vector transition distribution using chiral perturbation theory.
