Efficient multi-jet merging with the Vincia sector shower

We here present an extension of the CKKW-L multi-jet merging technique to so-called sector showers as implemented in the Vincia antenna shower. The bijective nature of sector showers allows for efficient multi-jet merging at high multiplicities, as any given configuration possesses only a single "history", while retaining the accuracy of the CKKW-L technique. Our method reduces the factorial scaling of the number of parton shower histories to a constant of a single history per colour-ordered final state. We show that the complexity of constructing shower histories is reduced to an effective linear scaling with the number of final-state particles. Moreover, we demonstrate that the overall event generation time and the memory footprint of our implementation remain approximately constant when including additional jets. We compare both to the conventional CKKW-L implementation in Pythia and gain a first estimate of renormalisation scale uncertainties at high merged multiplicities. As a proof of concept, we show parton-level predictions for vector boson production in proton-proton collisions with up to nine hard jets using the new implementation. Despite its much simpler nature, we dub the new technique MESS, in analogy to the conventional MEPS nomenclature.