Improvements on dipole shower colour

TL;DR

This paper enhances a dipole shower model by correcting sub-leading color effects and ensuring coherence, leading to more accurate simulations of QCD radiation patterns.

Contribution

It introduces a simple, efficient correction method for sub-leading color effects in dipole showers, improving their coherence properties.

Findings

The original shower inherits angular ordering from coherent branching.

Other dipole algorithms fail to maintain this angular coherence.

The correction aligns the shower's topology with QCD coherence at all orders.

Abstract

The dipole formalism provides a powerful framework from which parton showers can be constructed. In a recent paper, we proposed a dipole shower with improved colour accuracy and in this paper we show how it can be further improved. After an explicit check at $\mathcal{O}(\alpha_{\mathrm{s}}^{2})$ we confirm that our original shower performs as it was designed to, i.e. inheriting its handling of angular-ordered radiation from a coherent branching algorithm. We also show how other dipole shower algorithms fail to achieve this. Nevertheless, there is an $\mathcal{O}(\alpha_{\mathrm{s}}^{2})$ topology where it differs at sub-leading $N_{\mathrm{c}}$ from a coherent branching algorithm. This erroneous topology can contribute a leading logarithm to some observables and corresponds to emissions that are ordered in $k_t$ but not angle. We propose a simple, computationally efficient way to correct this and assign colour factors in accordance with the coherence properties of QCD to all orders in $\alpha_{\mathrm{s}}$.