Abstract
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.
Highlights
We find substantial merging scale dependencies induced by the enforced rapidity ordering in the default PYTHIA8 shower
Jets were defined with the k⊥-algorithm with D = 0.4
Curves with enforced rapidity ordering in the shower carry the label “y-ordered”, while results without explicit rapidity ordering are labelled “y-unordered”
Summary
We will present the main features of the Ckkw-l merging procedure. For a more detailed discussion of Ckkw-l and other similar merging algorithms we refer to [5, 6] and the original publications [7, 8]. To calculate the form factor we first have to reconstruct a parton-shower history for the states with n additional partons, S+n, given by the matrix element generator. The reweighting with Sudakov form factors proceeds by starting the parton shower at a given intermediate state S+i, setting ρi as the maximum scale, and generating one emission (ρ, z). The probability that this emission is above ρi+1 is exactly. Note that for initial-state parton-shower splittings, the no-emission probability Πis not the same as the Sudakov form factor needed to reweight the matrix-element generated state. In appendix A we elaborate on how the logarithmic accuracy of the shower is preserved in Ckkw-l and compare with the case of standard Ckkw using truncated showers
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