XCone: N-jettiness as an exclusive cone jet algorithm

Abstract

We introduce a new jet algorithm called XCone, for eXclusive Cone, which is based on minimizing the event shape N -jettiness. Because N -jettiness partitions every event into N jet regions and a beam region, XCone is an exclusive jet algorithm that always returns a fixed number of jets. We use a new "conical geometric" measure for which wellseparated jets are bounded by circles of radius R in the rapidity-azimuth plane, while overlapping jet regions automatically form nearest-neighbor "clover jets". This avoids the split/merge criteria needed in inclusive cone algorithms. A key feature of XCone is that it smoothly transitions between the resolved regime where the N signal jets of interest are well separated and the boosted regime where they overlap. The returned value of Njettiness also provides a quality criterion of how N -jet-like the event looks. We also discuss the N -jettiness factorization theorems that occur for various jet measures, which can be used to compute the associated exclusive N -jet cross sections. In a companion paper [1], the physics potential of XCone is demonstrated using the examples of dijet resonances, Higgs decays to bottom quarks, and all-hadronic top pairs.

Dichroic subjettiness ratios to distinguish colour flows in boosted boson tagging

“…with p = 1/2 [13,14]. The motivation behind this choice has been explained in [12] (see also [15,16]) and is related to the fact that, since it preserves the ordering in mass, it produces results very close to the much more complex minimal axes. 4 Since weak bosons radiate less than QCD jets, the ratio τ 21 = τ 2 /τ 1 is expected to be smaller for weak bosons and one imposes a cut τ 21 < τ cut as a radiation constraint to distinguish weak bosons from the QCD background.…”

Jet maximization, axis minimization, and stable cone finding

“…The minimum inside of T 1 partitions the event into an unclustered (or "beam") region and a jet region, and after minimizing overn, the jet region is exactly conical (for massless particles) with radius ≃ R. This approach has been generalized to Njettiness jet finding through the XCone jet algorithm [16,17].…”

“…In the jet function approach using (16), there are three candidate jets to consider: particle 1 alone, particle 2 alone, or particles 1 and 2 together. The corresponding jet function values are…”

“…Alternatively, one might be content with only finding a local T 1 minimum. For example, XCone [16,17] searches for local T 1 minima using IRC safe seeds based on k T -style clustering [21,22], leading to the clustering condition…”

“…The jet function approach is implemented with the J ET algorithm [5], which finds jets ordered by (30) but we take the hardest jet by p T . The 1-jettiness approach is implemented with XCone [16,17], using (31) with β = 2. 4 The stable cone approach is implemented with SISCone-PR [12,18], taking the hardest jet by p T .…”