Matching and event-shape NNDL accuracy in parton showers

TL;DR

This paper investigates how NLO matching techniques can enhance parton showers to achieve higher logarithmic accuracy, specifically NNDL, in event-shape observables and jet rates, through analytic and numerical methods.

Contribution

It demonstrates that NNDL accuracy can be attained in parton showers using straightforward matching methods like matrix-element corrections, MC@NLO, and POWHEG, advancing towards NNLL precision.

Findings

Matrix-element corrections achieve NNDL accuracy.

MC@NLO and POWHEG can also reach NNDL accuracy with proper implementation.

Careful handover in POWHEG is essential for maintaining accuracy.

Abstract

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 $q\bar q$ 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.