Recent Progress in Jet Algorithms and Their Impact in Underlying Event Studies

Matteo Cacciari^{1,2} 1LPTHE, UPMC – Paris 6, CNRS UMR 7589, Paris, France 2Université Paris-Diderot – Paris 7, Paris, France

Abstract

Recent developments in jet clustering are reviewed. We present a list of fast and infrared and collinear safe algorithms, and also describe new tools like jet areas. We show how these techniques can be applied to the study of underlying event or, more generally, of any background which can be considered distributed in a sufficiently uniform way.

1 Recent Developments in Jet Clustering

The final state of a high energy hadronic collision is inherently extremely complicated. Hundreds or even thousands of particles will be recorded by detectors at the Large Hadron Collider (LHC), making the task of reconstructing the original (simpler) hard event very difficult. This large number of particles is the product of a number of branchings and decays which follow the initial production of a handful of partons. Usually only a limited number of stages of this production process can be meaningfully described in quantitative terms, for instance by perturbation theory in QCD. This is why, in order to compare theory and data, the latter must first be simplified down to the level described by the theory.

Jet clustering algorithms offer precisely this possibility of creating calculable observables from many final-state particles. This is done by clustering them into jets via a well specified algorithm, which usually contains one or more parameters, the most important of them being a “radius” R which controls the extension of the jet in the rapidity-azimuth plane. One can also choose a recombination scheme, which controls how partons’ (or jets’) four-momenta are combined. The choice of a jet algorithm, its parameters and the recombination scheme is called a jet definition [1], and must be specified in full (together with the initial particles sample) in order for the process

{particles} ⟶^{jet definition} {jets}  (1)

to be fully reproducible and the final jets to be the same.

While (almost) any jet definition can produce sensible observables, not all of them will produce one which is calculable in perturbation theory. For this to be true, the jet algorithm must be infrared and collinear safe (IRC safe) [2], meaning that actions producing configurations that lead to divergences in perturbation theory, namely the emission of a very soft particle or a collinear splitting of a particle into two) must not produce any change in the jets returned by the algorithm.

The importance for jet algorithms to be IRC safe had been recognized as early as 1990 in the ‘Snowmass accord’ [3], together with the need for them to be easily applicable both on the