Matching Tree-Level Matrix Elements with Interleaved Showers

TL;DR

The paper implements the CKKW-L merging scheme to combine multi-jet tree-level matrix elements with PYTHIA8's transverse-momentum-ordered, interleaved showers, including interleaved multiple interactions. It validates the approach in e+e- and hadron-collision environments, quantifies merging-scale dependencies, and analyzes the impact of MI and unordered histories. A key finding is that enforced rapidity ordering in the default PYTHIA8 shower can induce substantial merging-scale dependencies and unitarity violations, which largely disappear when rapidity ordering is removed; the hardest jets are well modeled by matrix elements, while the shower handles softer emissions. The results imply that this merging framework is generally robust across processes like di-boson and QCD jet production, though retuning of PYTHIA8 parameters is recommended for optimal agreement with data, particularly for very hard 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.