Inclusive D production in $\gamma \gamma$ collisions: including the single-resolved contribution with massive quarks

We have calculated the next-to-leading order cross section for the inclusive production of charm quarks as a function of the transverse momentum p_T and the rapidity in two approaches using massive or massless charm quarks. For the single-resolved cross section we have derived the massless limit from the massive theory. We find that this limit differs from the genuine massless version with factorization by finite corrections. By adjusting subtraction terms we establish a massive theory with subtraction which approaches the massless theory very fast with increasing transverse momentum. With these results and including the equivalent results for the direct cross section obtained previously as well as double-resolved contributions, we calculate the inclusive cross section in collisions using realistic evolved non-perturbative fragmentation functions and compare with recent data from the LEP collaborations ALEPH, L3 and OPAL. We find good agreement. Received: 14 February 2003 / Published online: 5 May 2003