Planar Property and Long-range Azimuthal Correlation in $e^+e^-$ Annihilation

TL;DR

This paper analyzes azimuthal angle correlations in $e^+e^-$ annihilation events using high-order perturbative QCD, revealing significant planar properties and strong correlations that serve as benchmarks for studying collective effects in complex scattering processes.

Contribution

It provides the first detailed perturbative QCD calculation of long-range azimuthal correlations in $e^+e^-$ annihilation at NNLO, highlighting natural planar properties and energy-momentum conservation effects.

Findings

Significant planar properties observed in multi-jet events.

Strong azimuthal correlations consistent with energy-momentum conservation.

Benchmarks established for studying collective effects in high-energy collisions.

Abstract

The $e^+e^-$ annihilation of unpolarized beams is free from initial hadron states or initial anisotropy around the azimuthal angle, hence ideal for studying the correlations of dynamical origin via final state jets. We investigate the planar properties of the multi-jet events employing the relevant event-shape observables at next-to-next-to-leading order ($\mathcal{O}$($\alpha_{s}^{3}$)) in perturbative QCD; particularly, the azimuthal angle correlations on the long pseudo-rapidity (polar angle) range (Ridge correlation) between the inclusive jet momenta are calculated. We illustrate the significant planar properties and the strong correlations which are natural results of the energy-momentum conservation of the perturbative QCD radiation dynamics. Our study provides benchmarks of hard strong interaction background for the investigations on the collective and/or thermal effects via the Ridge-like correlation observables for complex scattering processes.