Two-parton scattering in the high-energy limit

Understand

Considering $2\to 2$ gauge-theory scattering with general colour in the high-energy limit, we compute the Regge-cut contribution to three loops through next-to-next-to-leading high-energy logarithms (NNLL) in the signature-odd sector.

• Our formalism is based on using the non-linear Balitsky-JIMWLK rapidity evolution equation to derive an effective Hamiltonian acting on states with a fixed number of Reggeized gluons.
• A new effect occurring first at NNLL is mixing between states with $k$ and $k+2$ Reggeized gluons due non-diagonal terms in this Hamiltonian.
• Our results are consistent with a recent determination of the infrared structure of scattering amplitudes at three loops, as well as a computation of $2\to 2$ gluon scattering in ${\cal N}=4$ super Yang-Mills theory.