Systematics of the Multi-Regge Three-Loop Symbol
Till Bargheer

TL;DR
This paper systematically analyzes the structure of three-loop scattering amplitude symbols in the multi-Regge limit, introducing new building blocks derived from known symbols and symmetry constraints to facilitate amplitude construction.
Contribution
It introduces a systematic method for constructing multi-Regge limit amplitudes at three loops using a finite set of building blocks derived from known symbols and symmetry considerations.
Findings
Two main building blocks are sufficient at leading logarithmic order.
The seven-point building block is constructed using single-valued multiple polylogarithms.
Additional subleading terms require extra building blocks or further perturbative data.
Abstract
We review the systematics of Mandelstam cut contributions to planar scattering amplitudes in the multi-Regge limit. Isolating the relevant cut terms, we explain how the BFKL expansion can be used to construct the perturbative n-point multi-Regge limit amplitude in certain kinematic regions from a finite number of basic building blocks. At three loops and at leading logarithmic order, two building blocks are required. Their symbols are extracted from the known three-loop six-point and seven-point symbols for general kinematics. The new seven-point building block is constructed in terms of single-valued multiple polylogarithms to the extent it can be determined using the symbol as well as further symmetry and consistency constraints. Beyond the leading logarithmic order, the subleading and sub-subleading terms require two and one further building block, respectively. The latter could…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
