Evaluating the 6-point Remainder Function Near the Collinear Limit

TL;DR

This paper advances the nonperturbative understanding of the 6-point remainder function in planar N=4 SYM theory near the collinear limit by extending integral computation methods to subleading terms and explicitly calculating up to 6 loops.

Contribution

It extends the integral computation method for the 6-point remainder function to subleading terms and provides explicit multi-loop results for the 2-gluon bound state contribution.

Findings

Proved the general form of the 2-gluon bound state contribution at any coupling.

Extended the integral method to compute subleading terms in the collinear expansion.

Provided explicit 6-loop expressions for the remainder function contributions.

Abstract

The simplicity of maximally supersymmetric Yang-Mills theory makes it an ideal theoretical laboratory for developing computational tools, which eventually find their way to QCD applications. In this contribution, we continue the investigation of a recent proposal by Basso, Sever and Vieira, for the nonperturbative description of its planar scattering amplitudes, as an expansion around collinear kinematics. The method of arXiv:1310.5735, for computing the integrals the latter proposal predicts for the leading term in the expansion of the 6-point remainder function, is extended to one of the subleading terms. In particular, we focus on the contribution of the 2-gluon bound state in the dual flux tube picture, proving its general form at any order in the coupling, and providing explicit expressions up to 6 loops. These are included in the ancillary file accompanying the version of this article on the arXiv.