Near-to-planar three-jet events at NNLL accuracy

Abstract

We extend the ARES method for next-to-next-to-leading-logarithmic (NNLL) QCD resummations to three-jet event shapes in e + e − collisions in the near-to-planar limit. In particular, we define a NNLL radiator for three hard emitters, and discuss new features of NNLL corrections arising specifically in this case. As an example, we present predictions for the D-parameter, matched to exact next-to-leading order (NLO). After inclusion of hadronisation corrections in the dispersive approach, we compare our predictions with LEP1 data.

Rings and strings: a basis for understanding subleading colour and QCD coherence beyond the two-jet limit

“…This particular limit of the three-jet coherence pattern is equivalent to what one would find by naively applying two-jet angular ordering. At present, relatively few precision analytic resummations of three (or more)-jet observables have been performed [27,30,46] (requiring the exponentiation of soft single logarithms). The prototypical three-jet observables [27,30] resum logarithms that measure the aplanarity of a process.…”

“…At present, relatively few precision analytic resummations of three (or more)-jet observables have been performed [27,30,46] (requiring the exponentiation of soft single logarithms). The prototypical three-jet observables [27,30] resum logarithms that measure the aplanarity of a process. These logarithms diverge when the jets lie exactly in a plane, analogous to thrust logarithms diverging for back-to-back, pencil-like jets 14 .…”

“…However, at their core, modern angular-ordered parton showers are still based on the early implementations of QCD coherence and their accuracy has not been systematically improved beyond the two-jet limit. Today, it is known that QCD coherence can be used to achieve NLL accuracy across a broad class of exponentiating observables beyond the two-jet limit (the rIRC safe observables) [26][27][28][29][30]. However, these insights have yet to be formulated as an algorithm that can be incorporated into a general purpose angular-ordered parton shower.…”

QCD at the FCC-ee

“…The perturbative description of kinematical regimes that require the all-order resummation of radiative corrections has also improved substantially in the past decade, and the state-of-the-art calculations for standard global event shapes and jet rates in e + e − → Z /γ * → q q + X are either NNLL or N 3 LL [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. Accurate predictions can be also obtained for e + e − → Z /γ * → q qg + X observables [56][57][58][59], particularly important for the study of gluon-initiated jets (and corresponding tuning of event generators). The computation of non-global observables [60], featuring angular cuts in the final state, poses a major theoretical challenge, and it is currently limited to lower logarithmic accuracy (see e.g.…”

Predictions to all orders in perturbative quantum chromodynamics for high energy collider experiments

“…For the three jet scale, calculations are available at high accuracy of NNLO+NNLL [354], achieved in the ARES [355,356] extension of the CAESAR formalism used in this thesis. The focus here will however be on reaching NLL accuracy for the higher multiplicities, where studies are limited to fixed order calculations at NNLO, while the resummation accuracy is limited [99,348].…”