Qjets: A Non-Deterministic Approach to Tree-Based Jet Substructure

TL;DR

It is found that employing a set of trees substantially reduces the observed fluctuations in the pruned mass distribution, enhancing the likelihood of new particle discovery for a given integrated luminosity.

Abstract

Jet substructure is typically studied using clustering algorithms, such as kT, which arrange the jets' constituents into trees. Instead of considering a single tree per jet, we propose that multiple trees should be considered, weighted by an appropriate metric. Then each jet in each event produces a distribution for an observable, rather than a single value. Advantages of this approach include: 1) observables have significantly increased statistical stability; and, 2) new observables, such as the variance of the distribution, provide new handles for signal and background discrimination. For example, we find that employing a set of trees substantially reduces the observed fluctuations in the pruned mass distribution, enhancing the likelihood of new particle discovery for a given integrated luminosity. Furthermore, the resulting pruned mass distributions for (background) QCD jets are found to be substantially wider than that for (signal) jets with intrinsic mass scales, e.g. jets containing a W decay. A cut on this width yields a substantial enhancement in significance relative to a cut on the standard pruned jet mass alone. In particular the luminosity needed for a given significance requirement decreases by a factor of two relative to standard pruning.

Figures (3)

• Figure 1: Distribution of pruned jet mass for a single QCD-jet with $p_T \sim 500~\text{GeV}$. The black and red solid lines show the classical pruned masses when $\text{C/A}$ and $k_T$ algorithms are used to cluster the jet. The black and dashed (red and dot-dashed) line shows the pruned jet mass distribution of 1000 trees (constructed from the same jet in the same event), when the $\text{C/A}$ ($\text{k}_{\text{T}}$) measure is used in Eq. \ref{['eq:shw']}. These distributions result from clusterings with rigidity $\alpha=1.0$ (top) and $\alpha=0.01$ (bottom).
• Figure 2: Distribution of volatility for signal (boosted $W$-jets) and background (QCD jets) using a rigidity $\alpha=0.01$.
• Figure 3: The background versus signal efficiencies corresponding to a cut on volatility, for various $\alpha$'s, as compared to the classical pruning result.