Generalized Fragmentation Functions for Fractal Jet Observables

Abstract

We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phenomenological implications. As an application, we present examples of fractal jet observables that are useful in discriminating quark jets from gluon jets.

37+18 pages, 24 figures

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• Extending Precision Perturbative QCD with Track Functions
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• Properties of jet fragmentation using charged particles measured with the ATLAS detector in $pp$ collisions at $\sqrt{s}=13$ TeV
• Phenomenology with a recoil-free jet axis: TMD fragmentation and the jet shape
• Non-Gaussianities in Collider Energy Flux
• Leading jets and energy loss
• Understanding Jet Charge
• Dark Sector Glueballs at the LHC
• Probing hadronization with flavor correlations of leading particles in jets
• The leading jet transverse momentum in inclusive jet production and with a loose jet veto
• Aspects of Track-Assisted Mass
• Safe but Incalculable: Energy-weighting is not all you need