A Brief Comment on Multi-Gluon Amplitudes and Double Parton Interactions

TL;DR

This paper analyzes multi-gluon amplitudes in the context of double parton interactions, revealing that dominant contributions are effectively two-body interactions rather than three-body, impacting understanding of gluon scattering processes.

Contribution

It provides a simplified analysis showing that multi-gluon amplitudes relevant to double parton interactions are dominated by two-body fusion processes, not enhanced in typical DPI configurations.

Findings

Color ordered amplitude not enhanced in typical DPI configurations.

Dominant contribution arises from fusion amplitude of two initial gluons.

Multi-gluon amplitude effectively describes a two-body interaction.

Abstract

A simplest case, where a contribution to a color ordered multi-gluon amplitude, describing a three body partonic interaction, can split into two weakly correlated two-body gluon scattering amplitudes and may thus contribute to a Double Parton Interaction, is briefly discussed. We find that the color ordered amplitude is not enhanced in the typical configuration generated by a DPI, where the transverse momenta of final state gluons are compensated pairwise, while a dominant contribution to the multi-gluon amplitude is due to terms proportional to the fusion amplitude of two initial state gluons. Which corresponds to an amplitude effectively describing a two rather than a three-body partonic interaction.