Final state dipole showers and the DGLAP equation

TL;DR

This paper demonstrates that a dipole-based final state parton shower in electron-positron annihilation correctly reproduces the DGLAP evolution equation for quark energy distributions, addressing previous concerns.

Contribution

It derives the DGLAP equation from a dipole shower model, confirming its consistency with established QCD evolution.

Findings

Derivation of the DGLAP equation from dipole shower dynamics

Confirmation that dipole showers reproduce known QCD evolution

Addresses and resolves prior concerns about dipole shower accuracy

Abstract

We study a parton shower description, based on a dipole picture, of the final state in electron-positron annihilation. In such a shower, the distribution function describing the inclusive probability to find a quark with a given energy depends on the shower evolution time. Starting from the exclusive evolution equation for the shower, we derive an equation for the evolution of the inclusive quark energy distribution in the limit of strong ordering in shower evolution time of the successive parton splittings. We find that, as expected, this is the DGLAP equation. This paper is a response to a recent paper of Dokshitzer and Marchesini that raised troubling issues about whether a dipole based shower could give the DGLAP equation for the quark energy distribution.