Photoproduction of isolated photon and jet at the DESY HERA

The next-to-leading order (NLO) QCD calculation for the isolated photon and isolated photon plus jet photoproduction at the ep collider DESY HERA is presented. The predictions for the isolated photon with no restrictions imposed on the jet are compared with the previous ones obtained in the small cone approximation, and the differences are found to be below 2%. The theoretical uncertainties in the cross section of the photoproduction of the photon plus jet are discussed. A short comparison with the new preliminary H1 data and with the NLO predictions of Fontannaz et al. is also presented.