Hexagon POPE: effective particles and tree level resummation

TL;DR

This paper develops a resummation method for the hexagon Wilson loop in planar N=4 SYM at tree level, using effective particles formed by flux tube excitations and small fermions, successfully reproducing the 6-point amplitude.

Contribution

It introduces a novel resummation approach using effective particles and measures at finite coupling, specifically applied at tree level for the hexagon Wilson loop.

Findings

Reproduces the 6-point tree level amplitude

Proposes measures for effective particles at finite coupling

Validates the resummation method at tree level

Abstract

We present the resummation of the full Pentagon Operator Product Expansion series of the hexagon Wilson loop in planar $\mathcal N=4$ SYM at tree level. We do so by considering the one effective particle states formed by a fundamental flux tube excitation and an arbitrary number of the so called "small fermions" which are then integrated out. We present our proposals for the one effective particle measures at finite coupling. By evaluating these measures at tree level and summing over all one effective particle states we reproduce the full 6 point tree level amplitude.