Solutions to the Balitsky-Kovchegov equation including the dipole orientation

Abstract

Solutions of the target-rapidity Balitsky-Kovchegov (BK) equation are studied considering, for the first time, the complete impact-parameter dependence, including the orientation of the dipole with respect to the impact-parameter vector. In our previous work, it has been demonstrated that the spurious Coulomb tails could be tamed using the collinearly-improved kernel and an appropriate initial condition in the projectile-rapidity BK equation. Introducing a different interpretation of the evolution variable, the target-rapidity formulation of the BK equation brings non-locality in rapidity and a kernel modification, removing the term that previously helped to suppress the Coulomb tails. To address this newly emerged non-locality, three different prescriptions are explored here to take into account the rapidities preceding the initial condition. Two of these approaches induce mild Coulomb tails, while the other is free from this effect within the studied rapidity range. The range is chosen to correspond to that of interest for existing and future experiments. To demonstrate that this set up can be used for phenomenological studies, the obtained solutions are used to compute the F2 structure function of the proton and the diffractive photo- and electro-production of J/ψ off protons. The predictions agree well with HERA data, confirming that the target-rapidity Balitsky-Kovchegov equation with the full impact-parameter dependence is a viable tool to study the small Bjorken-x limit of perturbative QCD at current facilities like RHIC and LHC as well as in future colliders like the EIC.