CCFM evolution with unitarity corrections

Abstract

We considerably extend our previous analysis of the implementation of an absorptive boundary condition, which mimics saturation effects, on the linear CCFM evolution. We present detailed results for the evolution of the unintegrated gluon density in the presence of saturation and extract the energy dependence of the emerging saturation momentum. We show that CCFM and BFKL evolution lead to almost identical predictions after including the effects of gluon saturation and of the running of the coupling. We moreover elucidate several important and subtle aspects of the CCFM formalism, such as its relation to BFKL, the structure of the angular ordered cascade, and the derivation of more inclusive versions of CCFM. We also propose non-leading modifications of the standard CCFM evolution which may play an important role for phenomenological studies.

Gluon saturation and final states

“…We expect the nonlinear term to be of main importance at low x similarly as in case of the BK equation. In this limit it will be of special interest to check whether in our formulation of the nonlinear extension of the CCFM equation one obtains an effect of saturation of the saturation scale as observed in [23] (for other formulations to include unitarity corrections in the CCFM evolution equation we refer the reader to [21,25]). This effect is of great importance since it has a consequences for example for imposing a bound on amount of produced entropy from saturated part of gluon density as observed in [26].…”

CCFM Evolution with Unitarity Bound

“…This implies that there is no unique equation to derive out of (4). The explicit choice for example used in the LDC model [12] (and this was also one of the choices in [2]) leads to the equation…”

“…In a series of studies, [1,2], we have proposed a method for effectively implementing saturation and unitarity within a generic linear evolution equation for the unintegrated gluon distribution, so like the BFKL [3] and the CCFM [4] equations. In these proceedings we shall summarise some of the results from [2] and we shall discuss prospects for the future and open questions.…”

“…In these proceedings we shall summarise some of the results from [2] and we shall discuss prospects for the future and open questions. For details of the topics to be presented here we refer to the cited articles.…”

“…They are related to corrections involving the eikonal and non-eikonal components of the three-gluon vertex. As shown in [2] one has at each vertex k…”