MHV amplitude for 3->3 gluon scattering in Regge limit

Abstract

We calculate corrections to the BDS formula for the six-particle planar MHV amplitude for the gluon transition 3->3 in the multi-Regge kinematics for the physical region, in which the Regge pole ansatz is not valid. The remainder function at two loops is obtained by an analytic continuation of the expression derived by Goncharov, Spradlin, Vergu and Volovich to the kinematic region described by the Mandelstam singularity exchange in the crossing channel. It contains both the imaginary and real contributions being in agreement with the BFKL predictions. The real part of the three loop expression is found from a dispersion-like all-loop formula for the remainder function in the multi-Regge kinematics derived by one of the authors. We also make a prediction for the all-loop real part of the remainder function multiplied by the BDS phase, which can be accessible through calculations in the regime of the strong coupling constant.

6 pages, 4 figures

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• BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at N=4 SUSY
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
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• The colour octet representation of the non-forward BFKL Green function
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• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
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• Gluon Reggeization in Yang-Mills Theories
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• Bootstrapping six-gluon scattering in planar $\mathcal{N}=4$ super-Yang-Mills theory
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• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• The four-loop six-gluon NMHV ratio function
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