BFKL and CCFM evolutions with saturation boundary

We perform numerical studies of the BFKL and CCFM equations for the unintegrated gluon distribution supplemented with an absorptive boundary which mimics saturation. For the BFKL equation, this procedure yields the same results for the saturation momentum and the gluon distribution above saturation as the non–linear BK equation, for both fixed and running coupling, and for all the considered energies. This similarity goes beyond expectations based on the correspondence with statistical physics, which hold only for fixed coupling and asymptotically high energies. For the CCFM equation, whose non–linear generalization is not known, our method provides the first study of the approach towards saturation. We find that, in the running–coupling case, the CCFM and BFKL predictions for the energy dependence of the saturation momentum are identical within our numerical accuracy. A similar saturation boundary could be easily implemented in the CCFM–based Monte Carlo event generators, so like CASCADE.