Non-linear evolution in CCFM: The interplay between coherence and saturation

TL;DR

This paper numerically solves the non-linear CCFM equation, revealing how coherence and saturation effects interplay to influence the saturation scale's dependence on rapidity and coherence momentum, with implications for deep inelastic scattering.

Contribution

It introduces a numerical solution to the non-linear CCFM equation that incorporates full dependence on the coherence scale and explores the resulting saturation dynamics.

Findings

Saturation scale depends on both rapidity and coherence momentum.

At high energies, the saturation momentum saturates due to non-linear and coherence effects.

Results are robust across different non-Sudakov form factors.

Abstract

We solve the CCFM equation numerically in the presence of a boundary condition which effectively incorporates the non-linear dynamics. We retain the full dependence of the unintegrated gluon distribution on the coherence scale, and extract the saturation momentum. The resulting saturation scale is a function of both rapidity and the coherence momentum. In Deep Inelastic Scattering this will lead to a dependence of the saturation scale on the photon virtuality in addition to the usual x-Bjorken dependence. At asymptotic energies the interplay between the perturbative non-linear physics, and that of the QCD coherence, leads to an interesting and novel dynamics where the saturation momentum itself eventually saturates. We also investigate various implementations of the "non-Sudakov" form factor. It is shown that the non-linear dynamics leads to almost identical results for different form factors. Finally, different choices of the scale of the running coupling are analyzed and implications for the phenomenology are discussed.