A new jet algorithm based on the k-means clustering for the reconstruction of heavy states from jets

TL;DR

The paper tackles miss-assignment in jet-based reconstruction of heavy-state decays by introducing a k-means clustering jet algorithm that can incorporate physics-driven criteria during clustering. It first analyzes an unconstrained version, showing improved mass resolution over the Durham algorithm at the cost of lower efficiency, and then introduces a constrained variant that combines clustering with kinematic priors to boost efficiency while maintaining resolution. Applications to all-hadronic top decays and WW decays at 500 GeV demonstrate narrower invariant-mass peaks and reduced shifts compared with traditional jet finders, with background studies indicating reduced risk of spurious peaks. The work suggests a promising direction for integrating prior physics information directly into jet clustering to improve heavy-state mass measurements, while acknowledging limitations such as detector effects and varying jet multiplicities for future exploration.

Abstract

A jet algorithm based on the k-means clustering procedure is proposed which can be used for the invariant-mass reconstruction of heavy states decaying to hadronic jets. The proposed algorithm was tested by reconstructing E+ E- to ttbar to 6 jets and E+ E- to W+W- to 4 jets processes at \sqrt{s}=500 GeV using a Monte Carlo simulation. It was shown that the algorithm has a reconstruction efficiency similar to traditional jet-finding algorithms, and leads to 25% and 40% reduction of reconstruction width for top quarks and W bosons, respectively, compared to the kT (Durham) algorithm. In addition, it is expected that the peak positions measured with the new algorithm have smaller systematical uncertainty.

Figures (3)

• Figure 1: The distribution of the trijet invariant masses for the reconstruction of all-hadronic top decays. Fully inclusive $e^+e^-$ events were generated with PYTHIA for $\sqrt{s}=500{\,\mathrm{GeV}}$. The reconstruction was done using the $k_T$ algorithm (left) and the $k$-means algorithm (right). The fit was performed using the Breit-Wigner function together with a second-order polynomial to describe the background.
• Figure 2: The dijet invariant masses for the all-hadronic top-decay channel. Fully inclusive $e^+e^-$ events were generated with PYTHIA for $\sqrt{s}=500{\,\mathrm{GeV}}$. The reconstruction was done using the constrained $k$-means algorithm (left). The fit was performed using the Breit-Wigner function together with a second-order polynomial to describe the background. The invariant masses reconstructed with the same algorithm using events without $t\bar{t}$ production does not have a spurious peak near the nominal top mass (right plot).
• Figure 3: The dijet reconstructed invariant masses for the all-hadronic $W$-decay channel $e^{+}e^{-}\to W^+W^-\to 4\, \mathrm{jets}$. The events containing fully hadronic $W^+W^-$ decays were generated with PYTHIA for $\sqrt{s}=500{\,\mathrm{GeV}}$. The reconstruction was done using the Durham algorithm (left) and the constrained $k$-means algorithm (right). The fit was performed using the Breit-Wigner function together with a second-order polynomial to describe the background.