  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/{\psi} 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.
