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 (42)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Gluon scattering amplitudes at strong coupling
• Multi-Parton Amplitudes in Gauge Theories
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Transcendentality and Crossing
• 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
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Multi-loop Amplitudes and Resummation
• Comments on gluon scattering amplitudes via AdS/CFT
• Hexagon Wilson loop = six-gluon MHV amplitude
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories
• The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order
• Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Next-to-leading Corrections to the BFKL Equation From the Gluon and Quark Production
• Gluon Regge Trajectory in the two-loop Approximation
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Sharpening The Leading Singularity
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Reggeization of quark-quark scattering amplitude in QCD
• Radiative corrections to quark-quark-reggeon vertex in QCD
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• From Trees to Loops and Back
• The high energy limit of QCD at two loops
• On the Gluon Regge Trajectory in $O({\alpha }_s^2)$
• Real next-to-leading corrections to the multigluon amplitudes in the helicity formalism
• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Equivalence of the Parke-Taylor and the Fadin-Kuraev-Lipatov amplitudes in the high-energy limit
• Implications of multi-Regge limits for the Bern-Dixon-Smirnov conjecture
• Parke-Taylor amplitudes in the multi-Regge kinematics
• Virtual Next-to-Leading Corrections to the Lipatov Vertex
• Analyticity for Multi-Regge Limits of the Bern-Dixon-Smirnov Amplitudes
• Virtual Next-to-Leading Corrections to the Impact Factors in the High-Energy Limit
• Testing high-energy factorization beyond the next-to-leading-logarithmic accuracy
• Next-to-Leading Corrections to the BFKL Equation

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