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Evaluating the 6-point Remainder Function Near the Collinear Limit

Georgios Papathanasiou

TL;DR

The paper addresses the nonperturbative structure of the planar six-point remainder function in maximally supersymmetric Yang-Mills theory, focusing on the collinear limit and the 2-gluon bound-state contribution within a flux-tube picture. It employs a residue-based reduction and Z-sum machinery to express results in harmonic polylogarithms, obtaining all-orders results and explicit expressions up to 6 loops. It validates these results against known collinear expansions of the full remainder function and provides new predictions for higher-loop terms, with data and formulas made available in ancillary files. The work advances computational tools for MSYM amplitudes and informs potential QCD applications by refining nonperturbative amplitude descriptions.

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.

Evaluating the 6-point Remainder Function Near the Collinear Limit

TL;DR

The paper addresses the nonperturbative structure of the planar six-point remainder function in maximally supersymmetric Yang-Mills theory, focusing on the collinear limit and the 2-gluon bound-state contribution within a flux-tube picture. It employs a residue-based reduction and Z-sum machinery to express results in harmonic polylogarithms, obtaining all-orders results and explicit expressions up to 6 loops. It validates these results against known collinear expansions of the full remainder function and provides new predictions for higher-loop terms, with data and formulas made available in ancillary files. The work advances computational tools for MSYM amplitudes and informs potential QCD applications by refining nonperturbative amplitude descriptions.

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.

Paper Structure

This paper contains 3 sections, 18 equations, 1 figure.

Table of Contents

  1. Introduction and Summary
  2. The 2-gluon bound state contribution
  3. Method and Results

Figures (1)

  • Figure 1: Left: The $n$-point MHV amplitude $A_n$ may be identified with a Wilson loop $W_n$ after defining dual space variables $k_i\equiv \textcolor{red}{x_{i+1}}-\textcolor{red}{x_i}\equiv x_{i+1,i}$. Since $k_i^2=0$, all distances between the cusps $x_i$ will be lightlike. Right: To take the collinear limit of $W_6$, we first connect two non-adjacent edges and form a square $(OPSF)$. It is invariant under three symmetries, and we act with one of them on $A$ and $B$, to flatten them on $(OF)$. We can then think of $(PO),(SF)$ as a color-electric flux tube sourced by $q\bar{q}$, and decompose $W_6$ w.r.t. its excitations $\psi_i$.