Iterated amplitudes in the high-energy limit

Abstract

We consider the high-energy limits of the colour ordered four-, five- and six-gluon MHV amplitudes of the maximally supersymmetric QCD in the multi-Regge kinematics where all the gluons are strongly ordered in rapidity. We show that various building blocks occurring in the Regge factorisation (the Regge trajectory, the coefficient functions and the Lipatov vertex) satisfy an iterative structure very similar to the Bern-Dixon-Smirnov (BDS) ansatz. This iterative structure, combined with the universality of the building blocks, enables us to show that in the Euclidean region any two- and three-loop amplitude in multi-Regge kinematics is guaranteed to satisfy the BDS ansatz. We also consider slightly more general kinematics where the strong rapidity ordering applies to all the gluons except the two with either the largest or smallest rapidities, and we derive the iterative formula for the associated coefficient function. We show that in this kinematic limit the BDS ansatz is also satisfied. Finally, we argue that only for more general kinematics - e.g. with three gluons having similar rapidities, or where the two central gluons have similar rapidities - can a disagreement with the BDS ansatz arise.

Version corresponding to the Erratum sent to JHEP on October 16th 2009

References in corpus (14)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
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• Sharpening The Leading Singularity
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
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Cited by in corpus (2)

• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes