The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit

TL;DR

This review discusses the behavior of scattering amplitudes in the multi-Regge limit for gauge theories like QCD and ${ m N}=4$ super-Yang-Mills, focusing on large logarithms, resummation techniques, and mathematical tools such as polylogarithms.

Contribution

It provides a comprehensive overview of recent progress in resumming large logarithms and applying advanced mathematical functions in the multi-Regge limit of gauge theories.

Findings

Progress in resumming next-to-next-to-leading logarithms in QCD

All-orders proposals for planar ${ m N}=4$ super-Yang-Mills theory

Application of single-valued multiple polylogarithms to scattering amplitudes

Abstract

We review the Regge and multi-Regge limit of scattering amplitudes in gauge theory, focusing on QCD and its maximally supersymmetric cousin, planar ${\cal N}=4$ super-Yang-Mills theory. We identify the large logarithms that are developed in these limits, and the progress that has been made in resumming them, towards next-to-next-to-leading logarithms for BFKL evolution in QCD, as well as all-orders proposals in planar ${\cal N}=4$ super-Yang-Mills theory and the perturbative checks of those proposals. We also cover the application of single-valued multiple polylogarithms to this important kinematical limit of particle scattering.