All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology

TL;DR

This paper uses symbol technology to derive a recursive formula for the leading imaginary part of all two-loop MHV amplitudes in multi-Regge kinematics in planar SYM theory, confirming predictions from BFKL calculations.

Contribution

It provides the first explicit recursive formula for the amplitude's imaginary part in multi-Regge kinematics using symbol technology, extending understanding of multi-loop amplitudes.

Findings

Derived a recursive structure for the amplitude's imaginary part.

Confirmed the recursive prediction with parallel BFKL computations.

Enhanced the analytic understanding of multi-loop amplitudes in specific kinematic limits.

Abstract

Recent progress on scattering amplitudes has benefited from the mathematical technology of symbols for efficiently handling the types of polylogarithm functions which frequently appear in multi-loop computations. The symbol for all two-loop MHV amplitudes in planar SYM theory is known, but explicit analytic formulas for the amplitudes are hard to come by except in special limits where things simplify, such as multi-Regge kinematics. By applying symbology we obtain a formula for the leading behavior of the imaginary part (the Mandelstam cut contribution) of this amplitude in multi-Regge kinematics for any number of gluons. Our result predicts a simple recursive structure which agrees with a direct BFKL computation carried out in a parallel publication.