  We show that, in onium-onium scattering at (very) high energy, a transition
to saturation happens due to quantum fluctuations of QCD dipoles. This
transition starts when the order $\alpha^2$ correction of the dipole loop is
compensated by its faster energy evolution, leading to a negative interference
with the tree level amplitude. After a derivation of the the one-loop dipole
contribution using conformal invariance of the elastic 4-gluon amplitude in
high energy QCD, we obtain an exact expression of the saturation line in the
plane (Y,L) where Y is the total rapidity and L, the logarithm of the onium
scale ratio. It shows universal features implying the Balitskyi - Fadin -
Kuraev - Lipatov (BFKL) evolution kernel and the square of the QCD triple
Pomeron vertex. For large L, only the higher BFKL Eigenvalue contributes,
leading to a saturation depending on leading log perturbative QCD
characteristics. For initial onium scales of same order, however, it involves
an unlimited summation over all conformal BFKL Eigenstates. In all cases,
conformal invariance is preserved for the saturation mechanism based on dipole
loops.
