Differences in binarity between gluon and graviton scattering amplitudes

TL;DR

This paper compares gluon and graviton scattering amplitudes, revealing fundamental differences in their binarity properties through on-shell diagram analysis and spinor-helicity formalism.

Contribution

It provides a detailed derivation of 3- and 4-point amplitudes for gluons and gravitons, highlighting the binarity in Yang-Mills theory and its absence in gravity.

Findings

Binarity is evident in pure Yang-Mills scattering amplitudes.

Gravity amplitudes show a reduced or absent binarity.

Differences suggest fundamental distinctions in the probability spaces of the two interactions.

Abstract

Both 3- and 4-point scattering amplitudes for spin-1 massless particles (gluons) and spin-2 massless particles (gravitons) are reviewed through self-contained step-by-step derivation. Gluon and graviton interactions are computed from on-shell diagrams by starting from complex momenta and introducing spinor-helicity formalism. By Fourier transforming spinor variables in momentum space, binarity is revealed in pure Yang-Mills scattering amplitudes while absent to a certain extent for gravity indicating fundamental differences in the probability spaces spanned by the two interactions.