Separated at Birth: Jet Maximization, Axis Minimization, and Stable Cone Finding

Abstract

Jet finding is a type of optimization problem, where hadrons from a high-energy collision event are grouped into jets based on a clustering criterion. As three interesting examples, one can form a jet cluster that (1) optimizes the overall jet four-vector, (2) optimizes the jet axis, or (3) aligns the jet axis with the jet four-vector. In this paper, we show that these three approaches to jet finding, despite being philosophically quite different, can be regarded as descendants of a mother optimization problem. For the special case of finding a single cone jet of fixed opening angle, the three approaches are genuinely identical when defined appropriately, and the result is a stable cone jet with the largest value of a quantity J. This relationship is only approximate for cone jets in the rapidity-azimuth plane, as used at the Large Hadron Collider, though the differences are mild for small radius jets.

7 pages, 2 tables; v2: references added; v3: small clarifications and table 2 added to match journal version

References in corpus (7)

• PYTHIA 6.4 Physics and Manual
• An Introduction to PYTHIA 8.2
• A practical Seedless Infrared-Safe Cone jet algorithm
• Jets in Hadron-Hadron Collisions
• Hadron Fragmentation Inside Jets in Hadronic Collisions
• Next-to-leading Order Calculation for Jets Defined by a Maximized Jet Function
• The Georgi Algorithms of Jet Clustering

Cited by in corpus (7)

• Quantum Algorithms for Jet Clustering
• XCone: N-jettiness as an Exclusive Cone Jet Algorithm
• The Hidden Geometry of Particle Collisions
• Disentangling Heavy Flavor at Colliders
• Resolving Boosted Jets with XCone
• Access to Photon Fragmentation Functions in Hadronic Jet Production
• Semi-Inclusive Jet Functions and Jet Substructure in $J_{E_T}^{(I)}$ and $J_{E_T}^{(II)}$ Algorithms