Systematics of the Multi-Regge Three-Loop Symbol

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 either be reconstructed from further perturbative data, or from BFKL integrals involving yet-unknown corrections to the central emission block.

34 pages, 88 diagrams; v2: added references, fixed typos, minor revision; v3: significant extension, new section on construction of the function g3, new appendix on four-loop decomposition, published version

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Cited by in corpus (5)

• All-order amplitudes at any multiplicity in the multi-Regge limit
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• All two-loop MHV remainder functions in multi-Regge kinematics
• Open Spin Chains and Complexity in the High Energy Limit
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills