Matching and event-shape NNDL accuracy in parton showers

To explore the interplay of NLO matching and next-to-leading logarithmic (NLL) parton showers, we consider the simplest case of gamma* and Higgs-boson decays to qq and gg respectively. Not only should shower NLL accuracy be retained across observables after matching, but for global event-shape observables and the two-jet rate, matching can augment the shower in such a way that it additionally achieves next-to-next-to double-logarithmic (NNDL) accuracy, a first step on the route towards general NNLL. As a proof-of-concept exploration of this question, we consider direct application of multiplicative matrix-element corrections, as well as simple implementations of MC@NLO and POWHEG-style matching. We find that the first two straightforwardly bring NNDL accuracy, and that this can also be achieved with POWHEG, although particular care is needed in the handover between POWHEG and the shower. Our study involves both analytic and numerical components and we also touch on some phenomenological considerations.

Automated summary

This study examines the relationship between NLO matching and NLL parton showers, focusing on the simplest case of gamma* and Higgs-boson decays to qq and gg. The study finds that matching can enhance the shower to achieve NNDL accuracy for global event-shape observables and the two-jet rate. Various methods, including multiplicative matrix-element corrections and MC@NLO and POWHEG-style matching, are explored and shown to bring NNDL accuracy. The study combines analytic and numerical components and also considers some phenomenological aspects.