Abstract
In this paper we show, that the $J/\psi$ production in DIS, is the main source of information about the events with two parton shower production. We attempt to develop our theoretical acumen of this process, to a level compatible with the theoretical description of inclusive DIS. We revisit the problem of the linear evolution equation for the double gluon densities, and include Bose-Einstein enhancement to these equations. We find that the Bose-Einstein correlations lead to an increase of the anomalous dimension, which turns out to be suppressed as $1/(N^2_c -1)^2$, in agreement with the estimates for the twist four anomalous dimension. We believe that understanding what happens to these contributions at ultra high energies, is a key question for an effective theory, based on high energy QCD. We derive the evolution equation for the scattering amplitude of two dipoles with a nucleus, taking into account the shadowing corrections, and investigate the analytical solutions in two distinct kinematic regions: deep in the saturation region, and in the vicinity of the saturation scale. The suggested non-linear evolution equation is a direct generalization of the Balitsky-Kovchegov equation, which has to be solved with the initial condition that depends on the saturation scale $Q_s(Y=Y_0,b)$. With the goal of finding a new small parameter, it is instructive to compare the solution of the non-linear equation with the qusi-classical approximation, in which in the initial condition we replace $Q_s(Y=Y_0,b)$ by $Q_s(Y,b)$. Our final result is that the shadowing corrections in the elastic amplitude generate the survival probability, which suppresses the growth of the amplitude with energy, caused by the Bose-Einstein enhancement.
Highlights
We show that the J=ψ production in DIS is the main source of information about the events with two-parton shower production
The suggested nonlinear evolution equation is a direct generalization of the Balitsky-Kovchegov equation, which has to be solved with the initial condition that depends on the saturation scale QsðY 1⁄4 Y0; bÞ
We believe that the process for the production of the J=ψ meson in the fragmentation region in DIS, is the simplest process aside from inclusive DIS, which allows us to investigate the scattering amplitudes in the wide kinematic region, from short distances which are the subject of perturbative QCD, to long distances of about 1=Qs (Qs is the saturation momentum), which can be described by the color glass condensate (CGC) approach(see Ref. [1] for a review)
Summary
We believe that the process for the production of the J=ψ meson in the fragmentation region in DIS, is the simplest process aside from inclusive DIS, which allows us to investigate the scattering amplitudes in the wide kinematic region, from short distances which are the subject of perturbative QCD, to long distances of about 1=Qs (Qs is the saturation momentum), which can be described by the color glass condensate (CGC) approach(see Ref. [1] for a review). The goal of this paper is to develop our theoretical understanding of J=ψ production, to a level compatible with the theoretical description of inclusive DIS At high energy this description includes the BFKL evolution equation [4] and the CGC/saturation approach for the scattering amplitude [5,6,7,8,9,10]. We wish to amend these equations, to include the Bose-Einstein enhancement, resulting from the correlations of identical gluons This effect has a suppression of the order of 1=ðN2c − 1Þ, where Nc is the number of colors, and is closely related to the 1=ðN21 − 1Þ corrections to the anomalous dimension of the twist-four operator, which is larger than the sum of the anomalous dimensions of two twist-two operators, as has been shown in Refs.
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