Jet Sampling: Improving Event Reconstruction through Multiple Interpretations

TL;DR

This work introduces Qanti-$k_T$, a non-deterministic extension of the anti-$k_T$ jet algorithm that samples multiple event-level interpretations to capture reconstruction ambiguity. By assigning each event a cut-weight $z$ and using weighted observables (and optional reweighting), the method improves signal significance $S/\delta B$ in complex topologies, sometimes substantially (e.g., up to 49% in resonance-pair scenarios and 28% in $ZH\to\nu\nu bb$ at 8 TeV). The approach preserves IRC safety for $\alpha>0$ and reduces sensitivity to the exact jet radius, offering a robust alternative to single-interpretation analyses. While slower for large samples, practical speedups are discussed, and the method shows clear advantages in overlapping/ambiguous jet configurations where traditional algorithms struggle.

Abstract

The classification of events involving jets as signal-like or background-like can depend strongly on the jet algorithm used and its parameters. This is partly due to the fact that standard jet algorithms yield a single partition of the particles in an event into jets, even if no particular choice stands out from the others. As an alternative, we propose that one should consider multiple interpretations of each event, generalizing the Qjets procedure to event-level analysis. With multiple interpretations, an event is no longer restricted to either satisfy cuts or not satisfy them - it can be assigned a weight between 0 and 1 based on how well it satisfies the cuts. These cut-weights can then be used to improve the discrimination power of an analysis or reduce the uncertainty on mass or cross-section measurements. For example, using this approach on a Higgs plus Z boson sample, with h->bb we find an 28% improvement in significance can be realized at the 8 TeV LHC. Through a number of other examples, we show various ways in which having multiple interpretations can be useful on the event level.

Figures (6)

• Figure 1: The top-left panel shows the $\eta \times\phi$ plot of a simulated $pp \to \phi\phi \to gggg$ event at the LHC, with $m_\phi = 500~\text{GeV}$. The top middle panel shows the jet areas associated with the four jets which best reconstruct the event using the classical anti-$k_T$ algorithm (see Sec. \ref{['sec:fourjets']}). The colors show the detector elements where zero-energy ghost particles would get clustered into each jet. The remaining plots show the frequency with which a cell is clustered into one of the four jets which best reconstruct each event for different choices of $\alpha$. Blue squares indicate a cell is nearly always included amongst the four hardest jets, green squares indicate that the cell is included roughly half the time, while pink indicates a cell is only rarely included. The same event is shown in all plots.
• Figure 2: The jet area computed using Qanti-$k_T$ for various choices of the rigidity parameter $\alpha$. Shown is the area of the hardest jet in $\phi\to gg$ dijet events with $m_\phi = 1$ TeV using $R=1.1$.
• Figure 3: $z$ is defined as the fraction of interpretations of an event satisfying a set of cuts. Shown is the distribution of $z$ for signal ($H+Z$ events, hollow, blue) and background ($Z+b\bar{b}$ events, solid, red) for various $\alpha$. The cuts used to calculate $z$ are $110~~\text{GeV}< m_{JJ} < 140~~\text{GeV}$ and $p_T > 25$ for each jet. Top-left shows the classical case, where an event either satisfies the cuts $z=0$ or it does not. Distributions are normalized to area 1. These normalized distributions are the functions $\rho(z)$ discussed in Sec. \ref{['sec:stats']}.
• Figure 4: $z$ is the fraction of interpretations of an event which satisfy the cuts, as in Fig \ref{['fig:f1s']}. The 2D distribution of $z$ as a function of the classical dijet mass $m_{JJ}$ is shown for some values of $\alpha$ for signal and background. Every event gives a value of $m_{JJ}$ and a value of $0 \le z \le 1$. Thus integrating over $z$ reproduces the classical $m_{JJ}$ distribution, as shown in the bottom right. In the classical limit $(\alpha \to \infty)$, information from multiple interpretations is inaccessible.
• Figure 5: A comparison of the signal (left) and background (right) dijet invariant mass distributions using standard anti-$k_T$ and Qanti-$k_T$ for optimized parameters. Signal is $Z\phi\to \nu \bar{\nu} gg$ with $m_\phi = 500~\text{GeV}$ and background is $Zgg\to\nu \bar{\nu} gg$. All events have ${\not\mathrel{E}}_T>800 ~\text{GeV}$ and $p_T > 400 ~\text{GeV}$ for each jet.