BFKL and CCFM evolutions with saturation boundary

TL;DR

This paper numerically compares BFKL and CCFM evolution equations with a saturation boundary, showing BFKL matches the non-linear BK results and providing new insights into CCFM's approach to saturation.

Contribution

It introduces a saturation boundary method for CCFM evolution and demonstrates its consistency with BFKL and BK equations across various conditions.

Findings

BFKL with saturation boundary matches BK equation results.

CFFM predictions for saturation momentum are similar to BFKL in running-coupling case.

First study of CCFM approach towards saturation.

Abstract

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.