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The Transition to Perturbative QCD in Compton Scattering

We investigate the transition to perturbative QCD in Compton processes, by concentrating on the specific reactions $πγ\to πγ$ and pion photoproduction at moderate energy scales. New sum rules for each of the helicities involved in the scattering and the cross section are given, together with a detailed stability analysis. Our results are then compared with those derived from higher-power factorization, incorporating Sudakov suppression for quark elastic scattering. An overlap of predictions obtained by the two approaches is observed at a momentum transfer as low as 4 GeV$^2$ and at a photon scattering angle around 40$^o$. Our work shows that factorization theorems and sum rule methods complement each other in the description of Compton scattering at moderate energy scales, and give information on the transition to perturbative QCD in these processes. The sum rule formalism is further applied to the crossed reaction $γγ\to π^+ π^-$, and is in very good agreement with the experimental data."