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 re
cent 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.
A recent, integrability-based conjecture in the framework of the Wilson loop OPE for N=4 SYM theory, predicts the leading OPE contribution for the hexagon MHV remainder function and NMHV ratio function to all loops, in integral form. We prove that th
ese integrals evaluate to a particular basis of harmonic polylogarithms, at any order in the weak coupling expansion. The proof constitutes an algorithm for the direct computation of the integrals, which we employ in order to obtain the full (N)MHV OPE contribution in question up to 6 loops, and certain parts of it up to 12 loops. We attach computer-readable files with our results, as well as an algorithm implementation which may be readily used to generate higher-loop corrections. The feasibility of obtaining the explicit kinematical dependence of the first term in the OPE in principle at arbitrary loop order, offers promise for the suitability of this approach as a non-perturbative description of Wilson loops/scattering amplitudes.
