Photoproduction of the isolated photon at DESY HERA in next-to-leading order QCD

The next-to-leading order (NLO) QCD calculation for the photoproduction of an isolated photon with a large $p_T$ at the $\mathrm{ep}$ collider DESY HERA is presented. The single resolved photon contribution and the QCD corrections of order ${\alpha }_s$ to the Born term are consistently included. The NNLO contributions, the box and double resolved photon subprocesses, are sizable and are taken into account in addition. The importance of the isolation cut as well as the influence of other experimental cuts on the $p_T$ and ${\eta }_{\gamma }$ (the final photon rapidity) distributions are discussed in detail. An investigation of the renormalization scale dependence is performed in order to estimate the size of missing higher order QCD corrections. The results are compared with experimental data and with the prediction of a different NLO calculation.