  We study two-to-two parton scattering amplitudes in the high-energy limit of
perturbative QCD by iteratively solving the BFKL equation. This allows us to
predict the imaginary part of the amplitude to leading-logarithmic order for
arbitrary $t$-channel colour exchange. The corrections we compute correspond to
ladder diagrams with any number of rungs formed between two Reggeized gluons.
Our approach exploits a separation of the two-Reggeon wavefunction, performed
directly in momentum space, between a soft region and a generic (hard) region.
The former component of the wavefunction leads to infrared divergences in the
amplitude and is therefore computed in dimensional regularization; the latter
is computed directly in two transverse dimensions and is expressed in terms of
single-valued harmonic polylogarithms of uniform weight. By combining the two
we determine exactly both infrared-divergent and finite contributions to the
two-to-two scattering amplitude order-by-order in perturbation theory. We study
the result numerically to 13 loops and find that finite corrections to the
amplitude have a finite radius of convergence which depends on the colour
representation of the $t$-channel exchange.
