Unintegrated gluon in the photon and heavy quark production

The unintegrated gluon density in the photon is determined, using the Kimber-Martin-Ryskin prescription. In addition, a model of the unintegrated gluon is proposed, based on the saturation model extended to the large-x region. These gluon densities are applied to obtain cross sections for charm and bottom production in gamma*p and gamma collisions using the k(t) factorization approach. We investigate both direct and resolved photon contributions and make a comparison with the results from the collinear approach and the experimental data. An enhancement of the cross section due to inclusion of non-zero transverse momenta of the gluons is found. The charm production cross section is consistent with the data. The data exceed our conservative estimate for bottom production in gammap collisions, but theoretical uncertainties are too large to claim a significant inconsistency. A substantial discrepancy between theory and the experiment is found for gamma --> b (b) over barX, which is not cured by the k(t) factorization approach.