Abstract
Considering 2 → 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 → 2 gluon scattering in mathcal{N} = 4 super Yang-Mills theory. Combining the latter with our Regge-cut calculation we extract the three-loop Regge trajectory in this theory. Our results open the way to predict high-energy logarithms through NNLL at higher-loop orders.
Highlights
Us to translate concepts from Regge theory [3] into calculation tools, leading to concrete predictions
While infrared factorization of fixed-angle scattering and high-energy factorization start from different kinematic set ups, and are based on different evolution equations, they lead to partially overlapping predictions for the structure of scattering amplitudes
Refs. [37, 38] showed that infrared factorization excludes the simplest form of Regge factorization where the amplitude in the high-energy limit is governed by a so-called Regge pole, and predicts that contributions associated with a Regge cut appear starting from the next-to-leading logarithmic (NLL) accuracy for the imaginary part of the amplitude and starting from the next-to-next-to-leading logarithmic (NNLL) accuracy for its real part
Summary
We write the perturbative expansion of a 2 → 2 scattering amplitude in the high-energy limit as. At NLL order, certain diagrams like (a) and (b) in figure 3 contribute only to the 8a colour structure but others like (c) and (d) contribute in addition to the even structures listed in eq (2.24) These signature-even contributions represent the exchange of a pair of Reggeized gluons and do not exponentiate in a simple way. More interesting are the corrections concerning the odd amplitude at NNLL accuracy, which, for this reason, are the focus of this paper In this case one has to take into account for the first time the exchange of three Reggeized gluons, as indicated by the right diagram in figure 4. Understanding these issues requires to investigate the structure of the amplitude in the context of the BFKL theory, which we are going to introduce
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