All two-loop MHV remainder functions in multi-Regge kinematics

Vittorio Del Duca,Brenda Penante,Falko Dulat,Claude Duhr

doi:10.1007/jhep01(2019)162

Abstract

We introduce a method to extract the symbol of the coefficient of (2πi)2 of MHV remainder functions in planar mathcal{N} = 4 Super Yang-Mills in multi-Regge kinematics region directly from the symbol in full kinematics. At two loops this symbol can be uplifted to the full function in a unique way, without any beyond-the-symbol ambiguities. We can therefore determine all two-loop MHV amplitudes at function level in all kinematic regions with different energy signs in multi-Regge kinematics. We analyse our results and we observe that they are consistent with the hypothesis of a contribution from the exchange of a three-Reggeon composite state starting from two loops and eight points in certain kinematic regions.

Highlights

Fully analytic results with more than six points are only known for the seven-point MHV remainder function [35]
We introduce a method to extract the symbol of the coefficient of (2πi)2 of MHV remainder functions in planar N = 4 Super Yang-Mills in multi-Regge kinematics region directly from the symbol in full kinematics
We analyse our results and we observe that they are consistent with the hypothesis of a contribution from the exchange of a three-Reggeon composite state starting from two loops and eight points in certain kinematic regions

Summary

Introduction

Fully analytic results with more than six points are only known for the seven-point MHV remainder function [35]. The study of amplitudes in particular kinematic limits is interesting as boundary data for the bootstrap program, but it is often the only way to gain analytic insight into the structure of scattering amplitudes with many loops and legs. These building blocks are described by resummed effective t-channel propagators (Reggeons) and the resummed emission of strongly-ordered gluons along the ladder of effective propagators They are determined to all orders from four- and five-point amplitudes which are completely fixed by symmetry, and Euclidean scattering amplitudes in MRK are trivial [55,56,57,58,59]. We obtain in this way complete analytic results for all two-loop MHV remainder functions in MRK in all Mandelstam regions By analysing explicit results through nine points, we observe that our results are consistent with the assumption of a contribution of a three-Reggeon composite state in certain Mandelstam regions, in agreement with the expectation from Regge theory

Objectives

Discussion

Conclusion