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Implementing the ME+PS merging algorithm

Andreas Schaelicke, Frank Krauss

TL;DR

This work presents a detailed ME+PS merging framework that combines tree-level matrix elements with parton showers to accurately describe multi-jet final states in both $e^+e^-$ annihilations and hadronic collisions. It extends previous methods by enabling competition between strong and electroweak amplitudes and by using a $k_ot$ jet measure to define jet regimes, with Sudakov reweighting to LL/NLL accuracy. The authors implement the algorithm in SHERPA, outlining the class structure and providing extensive examples and results across LEP and Tevatron processes, showing smooth, data-consistent predictions for jet rates and event shapes. They also introduce multi-cut and highest-multiplicity strategies to cover phase-space regions beyond available matrix elements and demonstrate correct treatment of electroweak-strong interference in four-jet final states, validating the approach's broad applicability and predictive power.

Abstract

The method to merge matrix elements for multi particle production and parton showers in electron-positron annihilations and hadronic collisions and its implementation into the new event generator SHERPA is described in detail. Examples highlighting different aspects of it are thoroughly discussed, some results for various cases are presented. In addition, a way to extend this method to general electroweak interactions is presented.

Implementing the ME+PS merging algorithm

TL;DR

This work presents a detailed ME+PS merging framework that combines tree-level matrix elements with parton showers to accurately describe multi-jet final states in both annihilations and hadronic collisions. It extends previous methods by enabling competition between strong and electroweak amplitudes and by using a jet measure to define jet regimes, with Sudakov reweighting to LL/NLL accuracy. The authors implement the algorithm in SHERPA, outlining the class structure and providing extensive examples and results across LEP and Tevatron processes, showing smooth, data-consistent predictions for jet rates and event shapes. They also introduce multi-cut and highest-multiplicity strategies to cover phase-space regions beyond available matrix elements and demonstrate correct treatment of electroweak-strong interference in four-jet final states, validating the approach's broad applicability and predictive power.

Abstract

The method to merge matrix elements for multi particle production and parton showers in electron-positron annihilations and hadronic collisions and its implementation into the new event generator SHERPA is described in detail. Examples highlighting different aspects of it are thoroughly discussed, some results for various cases are presented. In addition, a way to extend this method to general electroweak interactions is presented.

Paper Structure

This paper contains 24 sections, 19 equations, 24 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The algorithm
  3. Combination of matrix elements
  4. Pseudo parton shower history
  5. Starting the parton shower
  6. Examples
  7. Example I -- $e^+e^-\to \hbox{jets}$
  8. Example II -- $p \bar{p} \to W + \hbox{jets}$
  9. Example III -- $p \bar{p} \to \hbox{jets}$
  10. Example IV -- $e^+e^-\to d \bar{d} u \bar{u} (g)$
  11. Results
  12. Results for $e^+e^-\to \hbox{jets}$ at LEP I
  13. Results for $p\bar{p}\to W+\hbox{jets}$ at Tevatron, Run I
  14. Results for $p\bar{p}\to \hbox{jets}$ at Tevatron, Run I
  15. Results for $e^+e^-\to d \bar{d} u \bar{u} (g)$ at LEP II
  16. ...and 9 more sections

Figures (24)

  • Figure 1: The diagrams contributing to $e^+e^-\to 3\hbox{jets}$.
  • Figure 4: Examples for the production two and three jets.
  • Figure 5: Possible cluster configurations in $e^+e^-\to d \bar{d} u \bar{u} (g)$. The dashed line indicates the core $2 \to 2$ process.
  • Figure 6: Differential jet rates in the Durham scheme at LEP I. Shown are the results obtained through the merging of matrix elements for up to five jets with the parton shower, with two different separation cuts. The solid lines correspond to a cut at $y_{\rm cut}=10^{-2.5}$, and the dashed curve illustrates the result using $y_{\rm cut}=10^{-2}$. In the former case coloured lines indicate the contributions from individual matrix elements: two jets (red), three jets (green), four jets (blue), and five jets (purple).
  • Figure 7: Thrust (top left), thrust-major (top right), thrust minor (bottom left), and oblateness (bottom right) at LEP I. For definitions of these observables, cf. appendix \ref{['app:observables1']}. The hadron level result of SHERPA is pictured for two different separation cuts $y=10^{-2.5}$ and $y=10^{-2}$. Line styles and colours are the same as in Fig. \ref{['fig:lep_diffdurham1']}.
  • ...and 19 more figures