Nonlinear equation for coherent gluon emission

Abstract

Motivated by the regime of QCD explored nowadays at LHC, where both the total energy of collision and momenta transfers are high, we investigate evolution equations of high energy factorization. In order to study such effects like parton saturation in final states one is inevitably led to investigate how to combine physics of the BK and CCFM evolution equations. In this paper we obtain a new exclusive form of the BK equation which suggests a possible form of the nonlinear extension of the CCFM equation.

Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions

“…Essentially, this can be done by adding a µ 2 dependence to the unintegrated gluon distributions [29][30][31][51][52][53][54]. The equations that combine such effects with the small-x evolution [55,56] show a nontrivial interplay between the non-linearities and the µ 2 dependence and this may, in particular, weaken the saturation effects. At the linear level, the so-called single step inclusion of the hard-scale effects (as demonstrated in [17]) helps in the description of forward-central dijet data, therefore this direction seems to be relevant in order to provide complete predictions.…”

Resummation in nonlinear equation for high energy factorizable gluon density and its extension to include coherence

“…virtual contributions in the kernel, extend the BK to include coherence which is a step towards studies of exclusive observables [1]. The resummation performed in [1] transforms the full kernel (linear, and nonlinear part) of the equation to a form where so called Regge form factor multiplies full kernel.…”

“…The resummation performed in [1] transforms the full kernel (linear, and nonlinear part) of the equation to a form where so called Regge form factor multiplies full kernel. This result is highly non-trivial since, the equation was nonlinear, and the resummation technique was based on an integral transform method usually applicable to linear equations.…”

“…This result is highly non-trivial since, the equation was nonlinear, and the resummation technique was based on an integral transform method usually applicable to linear equations. The object for which the resummed equation was written was the so called WeizsackerWilliams gluon density (called in [1] dipole amplitude in the momentum space). This is one of the two basic densities which are used to construct densities used in studies of di-jets as derived in [12].…”

“…It turns out that although the nonlinear part of the equation for the unintegrated gluon density is much more complicated than the one studied in [1], one can perform still resummation analogously to [1], the results is the equation (3.9). The new form of the equation under consideration allows for the extraction of a more compact expression for the triple pomeron vertex without splitting the vertex into real and virtual terms which will most probably be easier to handle in future numerical simulations.…”