Telescoping jets: Probing hadronic event structure with multiple $R$’s

Jets at high energy colliders are complicated objects to identify. Even if jets are widely separated, there is no reason to define jets with the same size. A single reconstruction of each event can only extract a limited amount of information. While the Qjet algorithm gives multiple interpretations for each event using nondeterministic jet clustering, here we propose a simple, fast and powerful deterministic method to probe each event with multiple angular scales $R$’s in the jet definition. Though qualitatively a different approach, the information we get from reconstructions at different angular scales can be analyzed in the framework of multiple event interpretations. We show that the statistical power of an analysis can be dramatically increased. In particular, we can have a 46% improvement, as compared to 28% using Qjets, in the statistical significance of the Higgs search with a $Z$ boson ($ZH\to \nu \overline{\nu }b\overline{b}$) at the 8 TeV LHC. Our work implies that the wide angle radiation contains useful information, which is a key observation that is overlooked in both the conventional and the Qjet analyses.

Figure 1

A cartoon calorimeter plot distinguishing the width of the localized energy distribution of a jet (red) from the parameter $R$ (blue) in the anti-$k_T$ algorithm. $R$ is an artificial distance scale introduced to define the calorimeter region we want to look at. The jet axis points in the direction of the dominant energy flow, and the precise direction is not essential here.

Figure 2

Two $b$ jets with the same partonic kinematics but different widths, wider (top) and narrower (bottom).

Figure 3

The invariant mass distribution of the two $b$ jets for a $ZH$ event with multiple reconstructions using the telescoping jet algorithms (black). Using the anti-$k_T$ algorithm with $R=0.7$, $m_{jj}=143.4\mathrm{GeV}$ (red) which is outside the mass window of $110\mathrm{GeV}<m_{jj}<140\mathrm{GeV}$ in a conventional analysis. Multiple reconstructions reveal the ambiguity of this event and 37% of the reconstructions pass the cuts (blue).

Figure 4

The signal (top) and background (bottom) $m_{jj}$ distributions reconstructed using the anti-$k_T$ algorithm with $R=0.7$ (red), as well as the telescoping anti-$k_T$ (blue) and cone (green) algorithms (definitions explained in text). With multiple event reconstructions we get a wider signal Higgs mass peak, but it reduces the statistical fluctuations of the $m_{jj}$ distributions.

Figure 5

The signal and background $z$ distributions ${\rho }_S(z)$ and ${\rho }_B(z)$ using the telescoping anti-$k_T$ and cone algorithms. $z$ is the fraction of reconstructions of an event passing the experimental cuts. A large fraction of both signal and background events can be reconstructed differently.

Figure 6

The signal (blue) and background (red) volatility distributions using the telescoping cone algorithm.