Inclusive photoproduction of D* mesons with massive charm quarks

We have calculated the next-to-leading order cross sections for the inclusive production of D* mesons in γp collisions at HERA in two approaches using massive or massless charm quarks. The usual massive theory for the direct cross section with charm quarks only in the final state was transformed into a massive theory with MS subtraction by subtracting the mass divergent and additional finite terms calculated earlier in connection with the process γγ → D*X. This theory approaches the massless theory with increasing transverse momentum. The difference between the massive and the massless approach with MS subtraction is studied in detail in those kinematic regions relevant for comparison with experimental data. With these results and including the resolved cross section which is dominated by the part originating from the charm in the photon, we compute the fully inclusive D*± cross section and compare it with preliminary data from the ZEUS collaboration at HERA. We find on average good agreement. (orig.)