Next-to-leading-order corrections to inclusive hadron photoproduction

We present a complete calculation of next-to-leading-order corrections to inclusive hadron photoproduction. We take into account all contributions from resolved and unresolved photons and apply the results to ${\mathrm{\pi }}^0$ production at CERN LEP 2 as well as at the DESY ep collider HERA where we study in detail the scale dependence of the cross section. In addition compact analytical expressions for the matrix elements for all the direct contributions to both cross sections are presented. We also make a comparison with existing single tag data on inclusive charged hadron production.