QCD analysis of near-to-planar 3-jet events

TL;DR

This work develops an all-order perturbative QCD framework for the cumulative out-of-plane momentum in near-to-planar three-jet $e^+e^-$ events, achieving single-logarithmic accuracy by resumming soft-gluon radiation off the three-jet antenna and matching to $\,O(\alpha_s^2)$. The authors formulate a dipole-based radiator structure, derive both right-hemisphere and total $K_{out}$ distributions via Mellin-Fourier methods, and reveal how inter-jet coherence and event geometry enter the SL corrections through geometry-dependent scales. They provide explicit expressions for the radiators and SL prefactors, enabling precise predictions and paving the way to study non-perturbative power corrections in multi-jet topologies. The quasi-2-jet limit discussion clarifies how to interpolate between 3-jet and 2-jet configurations, highlighting the observable’s sensitivity to color topology and potential confinement effects.

Abstract

Perturbative QCD analysis is presented of the cumulative out-of-plane momentum distribution in the near-to-planar e+e- annihilation events, K_out << Q. In this kinematical region multiple gluon radiation effects become essential. They are resummed with the single-logarithmic accuracy, which programme includes the 2-loop treatment of the basic radiation and matching with the exact O(alpha_s^2) result. Dedicated experimental analyses of 3-jet event characteristics are of special interest for the study of the non-perturbative confinement effects.