Abstract
Abstract We introduce a jet shape observable defined for an ensemble of jets in terms of two-particle angular correlations and a resolution parameter R. This quantity is infrared and collinear safe and can be interpreted as a scaling exponent for the angular distribution of mass inside the jet. For small R it is close to the value 2 as a consequence of the approximately scale invariant QCD dynamics. For large R it is sensitive to non-perturbative effects. We describe the use of this correlation function for tests of QCD, for studying underlying event and pile-up effects, and for tuning Monte Carlo event generators.
Highlights
We would like to ask how this underlying event (UE) affects ∆G(R) for an ensemble of jets of a given pT
We introduce a jet shape observable defined for an ensemble of jets in terms of two-particle angular correlations and a resolution parameter R
We describe the use of this correlation function for tests of QCD, for studying underlying event and pile-up effects, and for tuning Monte Carlo event generators
Summary
It has long been appreciated that jets have a fractal-like structure. This point of view emerges naturally from the description of the parton shower as a probabilistic Markov chain. In particular they can be used to define fractal dimensions through their limiting behavior at small scales With this in mind, let us review the pair of correlation functions introduced in ref. In order to clearly observe scaling exponents, we will need to average over large ensembles of jets, since the number of final state particles in a single jet is too few to clearly observe fractal structure. Where N is the size of the ensemble and G(R)k is the angular correlation function of the kth jet From this average, we define the average angular structure function: Rd. where δdR(R) and ΘdR(R) are the gaussian and error functions with width dR, respectively.
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