Merging parton showers and matrix elements -- back to basics

TL;DR

This paper compares various methods of merging fixed-order matrix elements with parton-shower models, highlighting their strengths and weaknesses through a detailed analysis of the transition region in e+e- -> jets at order alpha_S.

Contribution

It provides a comprehensive comparison of merging schemes, identifying issues with scale definitions and shower ordering that affect the smoothness of the transition between matrix-element and parton-shower regions.

Findings

CKKW schemes offer a smooth transition when the shower is ordered in transverse momentum.

Problems arise if the parton shower is not ordered in transverse momentum.

Pseudo-Shower and MLM schemes have serious issues due to scale mismatches and initial condition sensitivities.

Abstract

We make a thorough comparison between different schemes of merging fixed-order tree-level matrix element generators with parton-shower models. We use the most basic benchmark of the O(alpha_S) correction to e+e- -> jets, where the simple kinematics allows us to study in detail the transition between the matrix-element and parton-shower regions. We find that the CKKW-based schemes give a reasonably smooth transition between these regions, although problems may occur if the parton shower used is not ordered in transverse momentum. However, the so-called Pseudo-Shower and MLM schemes turn out to have potentially serious problems due to different scale definitions in different regions of phase space, and due to sensitivity to the details in the initial conditions of the parton shower programs used.