Non-global jet evolution at finite N_c

TL;DR

The paper addresses non-global jet evolution at finite $N_c$ by exploiting a deep analogy with BK/JIMWLK in small-$x$ physics. It develops a functional Fokker–Planck framework and a Langevin description for a non-global evolution Hamiltonian $H_{ng}$, enabling finite-$N_c corrections to the Banfi–Marchesini–Smye equation. By constructing generating functionals for strongly ordered soft-gluon amplitudes and deriving transition probabilities via Gaussian averages, it derives an infinite hierarchy of coupled evolution equations for soft semi-inclusive quantities, reducing to BMS/BK in the appropriate limits. The work thus provides a principled path to numerically study non-global jet observables at finite color number and suggests potential cross-fertilization with CGC methods for broader QCD applications.

Abstract

Resummations of soft gluon emissions play an important role in many applications of QCD, among them jet observables and small x saturation effects. Banfi, Marchesini, and Smye have derived an evolution equation for non-global jet observables that exhibits a remarkable analogy with the BK equation used in the small x context. Here, this analogy is used to generalize the former beyond the leading N_c approximation. The result shows striking analogy with the JIMWLK equation describing the small x evolution of the color glass condensate. A Langevin description allows numerical implementation and provides clues for the formulation of closed forms for amplitudes at finite N_c. The proof of the new equation is based on these amplitudes with ordered soft emission. It is fully independent of the derivation of the JIMWLK equation and thus sheds new light also on this topic.