  In the scattering of a small onium off a large nucleus at high center-of-mass
energies, when the parameters are set in such a way that the cross section at
fixed impact parameter is small, events are triggered by rare partonic
fluctuations of the onium, which are very deformed with respect to typical
configurations. Using the color dipole picture of high-energy interactions in
quantum chromodynamics, in which the quantum states of the onium are
represented by sets of dipoles generated by a branching process, we describe
the typical scattering configurations as seen from different reference frames,
from the restframe of the nucleus to frames in which the rapidity is shared
between the projectile onium and the nucleus. We show that taking advantage of
the freedom to select a frame in the latter class makes possible to derive
complete asymptotic expressions for some boost-invariant quantities, beyond the
total cross section, from a procedure which leverages the limited available
knowledge on the properties of the solutions to the Balitsky-Kovchegov equation
that governs the rapidity-dependence of total cross sections. We obtain in this
way an analytic expression for the rapidity-distribution of the first branching
of the slowest parent dipole of the set of those which scatter. This
distribution provides an estimator of the correlations of the interacting
dipoles, and is also known to be related to the rapidity-gap distribution in
diffractive dissociation, an observable measurable at a future electron-ion
collider. Furthermore, our result may be formulated as a more general
conjecture, that we expect to hold true for any one-dimensional branching
random walk model, on the branching time of the most recent common ancestor of
all the particles that end up to the right of a given position.
