Progress in calculating hexagon amplitudes at one-loop

TL;DR

Problem: derive analytic one-loop corrections for massless 6-point amplitudes (hexagon) relevant for NLO multi-jet processes. Approach: study simplified Yukawa-model amplitudes to reveal organizing principles, employing scalar reduction, reduction coefficients B_k, and projection techniques to handle tensor structures. Key contributions: a compact expression for the 6-scalar Yukawa amplitude built from triangle and log terms with IR cancellations, and a tensor-structure ++ helicity amplitude for γγ → 4 scalars expressed via reduction-coefficient-based building blocks; demonstration that hexagon amplitudes can be represented as linear combinations of reduction coefficients. Significance: provides structural insight and practical reduction strategies toward NLO 2→4 predictions at colliders, while acknowledging that full QCD extensions remain to be developed.

Abstract

In this article I review recent progress towards the analytical calculation of massless 6--point amplitudes. A way to organize such calculations is sketched and results for scattering amplitudes in the Yukawa model are presented.