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 $1/(N_c^2-1{)}^2$, 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 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 $Q_s(Y=Y_0,b)$. With the goal of finding a new small parameter, it is instructive to compare the solution of the nonlinear 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.

• Received 1 May 2018

DOI:https://doi.org/10.1103/PhysRevD.98.034014

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Published by the American Physical Society