Jet Observables Without Jet Algorithms

TL;DR

The paper introduces jet-like event shapes that recast jet observables as infrared/collinear-safe sums over all final-state particles within local cones of radius $R$ and a threshold $p_{T\text{cut}}$. It defines $\widetilde{N}_{\text{jet}}$, $\widetilde{H}_T$, and $\widetilde{\slashed{p}}_T$ and demonstrates their correlation with standard jet-based measures through MC studies, while producing continuous, non-integer values that reflect jet-definition ambiguities. It then shows how to invert $\widetilde{N}_{\text{jet}}$ to estimate the $p_T$ of the $n$-th hardest jet without explicit jet finding, and introduces a hybrid density with winner-take-all recombination to recover jet constituents. The framework is further extended to shape trimming for event-wide grooming, with generalizations to subjet-like observables, offering potential trigger-level applications and pathways for analytic QCD exploration of jet-like phenomena.

Abstract

We introduce a new class of event shapes to characterize the jet-like structure of an event. Like traditional event shapes, our observables are infrared/collinear safe and involve a sum over all hadrons in an event, but like a jet clustering algorithm, they incorporate a jet radius parameter and a transverse momentum cut. Three of the ubiquitous jet-based observables---jet multiplicity, summed scalar transverse momentum, and missing transverse momentum---have event shape counterparts that are closely correlated with their jet-based cousins. Due to their "local" computational structure, these jet-like event shapes could potentially be used for trigger-level event selection at the LHC. Intriguingly, the jet multiplicity event shape typically takes on non-integer values, highlighting the inherent ambiguity in defining jets. By inverting jet multiplicity, we show how to characterize the transverse momentum of the n-th hardest jet without actually finding the constituents of that jet. Since many physics applications do require knowledge about the jet constituents, we also build a hybrid event shape that incorporates (local) jet clustering information. As a straightforward application of our general technique, we derive an event-shape version of jet trimming, allowing event-wide jet grooming without explicit jet identification. Finally, we briefly mention possible applications of our method for jet substructure studies.

Figures (18)

• Figure 1: Instead of defining inclusive jet observables by summing over jet regions according to a jet algorithm (left), our event shapes sum over the contributions from cones of radius $R$ centered on each particle $i$ (right). The weight factor $p_{Ti}/p_{Ti,R}$ in Eq. (\ref{['eq:generalForm']}) avoids double-counting despite overlapping cones. For infinitely narrow jets separated by more than $R$, the two methods yield the same result.
• Figure 2: Jet multiplicity (i.e. $N_{\text{jet}}$) for QCD dijet events. Fig. \ref{['fig:HistoNj']} shows the distribution of the number of anti-$k_T$ jets with $R=0.6$ and $p_{T{\rm cut}}=25$ GeV (green dashed curve), and of the corresponding event shape with the same values of $R$ and $p_{T{\rm cut}}$ (red curve). Only events with $N_\text{jet}\geq 1$ or $\widetilde{N}_\text{jet}\geq 0.5$ are shown, and a parton level cut of $p_{T\text{cut}}^\text{parton}=25~\text{GeV}$ is employed to give a reasonable sample of both one jet and two jet events. Whereas $N_{\text{jet}}$ takes on only integer values, the event shape $\widetilde{N}_{\text{jet}}$ is continuous, albeit with spikes near integer values. Fig. \ref{['fig:ScatterNj']} shows the correlation between the two observables, where the area of the squares is proportional to the fraction of events in each bin. In the correlation plot, events that fail one of the jet cut criteria are assigned the corresponding value of zero.
• Figure 3: Summed scalar transverse momentum (i.e. $H_T$) for QCD dijet events. The jet parameters, formatting, and cuts are the same as for Fig. \ref{['fig:Njet']}. Because of the smoother behavior of the event shape $\widetilde{H}_T$, the peaks rising at $p_{T{\rm cut}}$ and $2\, p_{T{\rm cut}}$ are less pronounced than for $H_T$.
• Figure 4: Missing transverse momentum (i.e. $\slashed{p}_T$) for $Z(\rightarrow \nu\bar{\nu})+j$ events. The jet parameters, formatting, and cuts are the same as for Fig. \ref{['fig:Njet']}. Again, we see a smoother turn on behavior for $\widetilde{\slashed{p}}_T$ compared to $\slashed{p}_T$.
• Figure 5: Average jet transverse momentum (i.e. $H_T$ divided by $N_\text{jet}$) for QCD dijet events. The jet parameters, formatting, and cuts are the same as for Fig. \ref{['fig:Njet']}.