Matching Tree-Level Matrix Elements with Interleaved Showers

TL;DR

This paper implements and validates a scheme for merging multi-jet matrix elements with parton showers in PYTHIA8, analyzing the effects of rapidity ordering and underlying event modeling on observable predictions.

Contribution

The paper introduces a detailed implementation of the CKKW-L merging scheme within PYTHIA8, including validation and analysis of algorithmic details affecting observables.

Findings

Merging scale dependence is significant with default rapidity ordering.

Removing rapidity ordering reduces merging scale dependence.

The shower accurately models multi-jet event hardness when matrix elements set the hardest jets.

Abstract

We present an implementation of the so-called CKKW-L merging scheme for combining multi-jet tree-level matrix elements with parton showers. The implementation uses the transverse-momentum-ordered shower with interleaved multiple interactions as implemented in PYTHIA8. We validate our procedure using e+e--annihilation into jets and vector boson production in hadronic collisions, with special attention to details in the algorithm which are formally sub-leading in character, but may have visible effects in some observables. We find substantial merging scale dependencies induced by the enforced rapidity ordering in the default PYTHIA8 shower. If this rapidity ordering is removed the merging scale dependence is almost negligible. We then also find that the shower does a surprisingly good job of describing the hardness of multi-jet events, as long as the hardest couple of jets are given by the matrix elements. The effects of using interleaved multiple interactions as compared to more simplistic ways of adding underlying-event effects in vector boson production are shown to be negligible except in a few sensitive observables. To illustrate the generality of our implementation, we also give some example results from di-boson production and pure QCD jet production in hadronic collisions.