The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

Abstract

We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the 2->5 amplitude in planar N=4 super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop N-particle MHV amplitude in this region to a function, we specialize to N=7, and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the building block of the dispersion integral that had not yet appeared in the well-studied six-gluon case. As an application of our results, we explicitly compute the seven-gluon amplitude at next-to-leading logarithmic accuracy through 5 loops for the MHV case, and through 3 and 4 loops for the two independent NMHV helicity configurations, respectively.

56 pages, 4 figures, 1 table; v2: minor corrections and clarifications, matches published version

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• How tropical are seven- and eight-particle amplitudes?
• Lifting Heptagon Symbols to Functions
• All-order amplitudes at any multiplicity in the multi-Regge limit
• Inclusive prompt photon production in electron-nucleus scattering at small x
• Anomalous Dimensions from Soft Regge Constants
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• All two-loop MHV remainder functions in multi-Regge kinematics
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• The two-loop Higgs impact factor
• The long road from Regge poles to the LHC
• The Multi-Regge Limit from the Wilson Loop OPE
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• A tale of two Regge limits