Some remarks on dipole showers and the DGLAP equation

TL;DR

This paper demonstrates that dipole shower algorithms can be consistent with the DGLAP equation when using appropriate evolution variables, countering recent claims of conflict.

Contribution

It clarifies that the choice of evolution variable is crucial and shows numerically that dipole showers can reproduce DGLAP evolution accurately.

Findings

Dipole showers with proper evolution variables reproduce DGLAP equations.

Incorrect assumptions about gluon energy as evolution variable lead to false conflicts.

Monte Carlo simulations match second-order QCD matrix elements in asymptotic behavior.

Abstract

It has been argued recently that parton showers based on colour dipoles conflict with collinear factorization and do not lead to the correct DGLAP equation. We show that this conclusion is based on an inappropriate assumption, namely the choice of the gluon energy as evolution variable. We further show numerically that Monte Carlo programs based on dipole showers with "infrared sensible" evolution variables reproduce the DGLAP equation both in asymptotic form as well as in comparison to the leading behaviour of second-order QCD matrix elements.