[Paper Review] J_{E_T}: A Global Jet Finding Algorithm

Y. Bai, Zhenyu Han+1 more|arXiv (Cornell University)|Nov 13, 2014

Particle physics theoretical and experimental studies13 references3 citations

TL;DR

This paper introduces $J_{E_T}$, a global jet-finding algorithm for hadron colliders that maximizes a function balancing jet transverse energy and mass to produce circular-cone jets with geometric centers shifted toward the central region. The algorithm achieves infrared and collinear safety, exhibits cone size reduction in forward regions, and demonstrates higher efficiency than anti-$k_t$ in identifying $W$-jets with hard splittings when matched via QCD jets.

ABSTRACT

We introduce a new jet-finding algorithm for a hadron collider based on maximizing a J_{E_T} function for all possible combinations of particles in an event. This function prefers a larger value of the jet transverse energy and a smaller value of the jet mass. The jet shape is proved to be a circular cone in Cartesian coordinates with the geometric center shifted from the jet momentum toward the central region. The jet cone size shrinks for a more forward jet. We have implemented our J_{E_T} algorithm with a reasonable running time scaling as N n^3, where "N" is the total number of particles and "n" (much less than N) is the number of particles in a fiducial region. Many features of our J_{E_T} jets are similar to anti-k_t jets, including the reconstructed jet momentum and the "back-reaction" from soft contamination. Nevertheless, when the jet parameters in the two algorithms are matched using QCD jets, we find that the J_{E_T} algorithm has a larger efficiency than anti-k_t for identifying objects with hard splittings such as a W-jet.

Motivation & Objective

• To develop a new global jet-finding algorithm for hadron colliders that improves jet reconstruction for boosted objects like $W$-jets.
• To address limitations in existing cone and recombination algorithms by introducing a function-based approach that ensures infrared and collinear safety.
• To achieve a jet shape that naturally suppresses forward contamination while preserving high efficiency for hard splittings.
• To provide a computationally feasible alternative to exhaustive subset searches by leveraging geometric constraints and spherical circle enumeration.

Proposed method

• The algorithm maximizes the $J_{E_T} = E_T - \beta m_J^2 / E_T$ function over all particle subsets to identify the optimal jet configuration.
• It proves that $J_{E_T}$ jets form circular cones in Cartesian coordinates, with the cone axis shifted from the jet momentum toward the transverse direction.
• The cone size shrinks in the forward region due to the $\beta$-dependent geometric center shift, effectively suppressing beam-parallel clustering.
• The search space is reduced by considering only circles defined by three or two particles on the unit sphere, analogous to SISCone’s approach.
• The algorithm is implemented with $O(Nn^3)$ scaling, where $N$ is total particles and $n \ll N$ is particles in a fiducial region.
• A generalized $J_{E_T^\alpha}$ function is introduced to explore different mass-weighting behaviors, with $\alpha=1$ recovering $J_{E_T}$.

Experimental results

Research questions

• RQ1 Can a global jet-finding algorithm based on maximizing a transverse energy-to-mass ratio produce stable, physically motivated jet shapes with inherent forward suppression?
• RQ2 How does the $J_{E_T}$ algorithm compare to established algorithms like anti-$k_t$ and SISCone in reconstructing $W$-jets with hard splittings?
• RQ3 What is the impact of the geometric center shift and cone size variation on jet shape and pileup resilience?
• RQ4 Can the $J_{E_T}$ algorithm maintain high efficiency for $W$-jet tagging while ensuring infrared and collinear safety?
• RQ5 To what extent can the algorithm’s performance be tuned via the $\beta$ parameter and extended with split-merge procedures?

Key findings

• The $J_{E_T}$ algorithm produces circular-cone jets whose geometric centers are shifted toward the transverse plane, with the shift increasing for forward jets.
• The cone size shrinks in the forward region due to the $\beta$-dependent geometric center shift, effectively suppressing beam-parallel clustering.
• The algorithm is infrared and collinear safe because $J_{E_T}$ depends only on the jet four-momentum, not on individual particle momenta.
• When matched to anti-$k_t$ using QCD dijets, $J_{E_T}$ achieves higher $W$-jet identification efficiency, particularly for hard splittings.
• For $W$-jet tagging, $J_{E_T}$ outperforms SISCone with $f=0.99$ but underperforms SISCone with $f=0.75$, indicating potential for improvement via split-merge extensions.
• The $J_{E_T^\alpha}$ generalization allows tuning of mass suppression behavior, with $\alpha=2$ requiring $\beta>2$ for fiducial region particle exclusion.