The equivalence between the color dipole model and the BFKL Pomeron at leading order

We compute the onium-onium scattering amplitude at fixed impact parameter in the framework of the perturbative QCD dipole model. Relying on the conformal properties of the dipole cascade and of the elementary dipole-dipole scattering amplitude, we obtain an exact result for this onium-onium scattering amplitude, which is proved to be identical to the BFKL result, and which is frame invariant. The asymptotic expression for this amplitude at fixed impact parameter agrees with previous numerical simulations.