The deep compton scattering: Single photon spectrum and photon-hadron correlations beyond leading logarithms

We have calculated higher order QCD corrections to the Deep Inelastic Compton single inclusive cross-section. The perturbation expansion seems to be well behaved: the corrections are small and the fully corrected cross-section depends little on the factorization scale which is chosen. A complete phenomenological study at SPS, Tevatron and HERA energies is performed and theoretical predictions tend to be in good agreement with preliminary experimental data. The corrections to the double inclusive cross-section sigma(γp->γhX) are also calculated and found to be small in the region of physical interest for sigma(γp->γπ+X)-sigma(γp->γπ-X). (orig.)