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Jet finding is a type of optimization problem, where hadrons from ahigh-energy collision event are grouped into jets based on a clusteringcriterion. 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 thesethree approaches to jet finding, despite being philosophically quite different,can be regarded as descendants of a mother optimization problem. For thespecial case of finding a single cone jet of fixed opening angle, the threeapproaches are genuinely identical when defined appropriately, and the resultis a stable cone jet with the largest value of a quantity J. This relationshipis only approximate for cone jets in the rapidity-azimuth plane, as used at theLarge Hadron Collider, though the differences are mild for small radius jets.

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