Review on recent developements in jet finding
We review recent developements related to jet clustering algorithms and jet finding. These include fast implementations of sequential recombination algorithms, new IRC safe algorithms, quantitative determination of jet areas and quality measures for jet finding, among many others. We also briefly discuss the status of jet finding in heavy ion collisions, where full QCD jets have been measured for the first time at RHIC.
Review on recent developements in jet finding
LPTHE, UPMC – Paris 6 and Paris-Diderot – Paris 7, CNRS UMR 7589, Paris (France)
INFN, Sezione di Milano, Via Celoria 16, I - 20133, Milano (Italy)
Recent developements in jet algorithms
With the upcoming start-up of the LHC, jet finding techniques have received considerable attention. In this brief review, we outline some of the most important developements in jet algorithms and related subjects in the recent years. Much more detailed reviews can be found in [1, 2].
An important developement has been the fast implementation of the  and Cambridge/Aachen [4, 5] jet algorithms. Prior to 2005, existing implementations scaled as , with the number of particles to be clustered, thus making it unpractical for high multiplicity collisions like at the LHC and even more in Heavy Ions Collisions (HIC). Thanks to computational geometry methods, the performance of these algorithms was made to scale as . These fast implementations are available through the FastJet package , together with area-based subtraction methods and plugins to external jet finders (see below).
Another important achievement has been the formulation of a practical (scaling as ) infrared and collinear (IRC) safe cone algorithm, SISCone . Unlike all other commonly used cone algorithms, SISCone is IRC safe to all orders in perturbation theory by construction. This property allows one to compare any perturbative computation with experimental data, which for IRC unsafe algorithms is impossible beyond some fixed order, indicated in Fig. 2. As discussed in , the phenomenological implications of SISCone when compared with the (IRC unsafe) commonly used MidPoint cone algorithm range from few percent differences in the inclusive jet spectrum, somewhat larger in the presence of realistic Underlying Event (UE), up to 50% differences for more exclusive observables, like the tails of jet-mass spectra in multi-jet events.
There has been historically some confusion about the concept of the size of a jet, specially since the naive jet area is ambiguous beyond LO. The situation was recently clarified by the introduction of quantitative definitions of jet areas based on the catchment properties of hard jets with respect to very soft particles, called ghosts in . Examples of jet areas defined with such a technique are shown in Fig. 1. On top of their theoretical importance, jet areas have important applications related to the subtraction of soft backgrounds coming from the UE or from Pile-Up (PU), both in and in collisions, as discussed in .
Another recently developed IRC safe jet algorithm is the anti- algorithm . This algorithm is related to and Cam/Aa by its distance measure, , with ( corresponds to and to Cam/Aa). The anti- algorithm has the property of being soft-resilient, that is, due to its distance soft particles are always clustered with hard particles first. This property leads to rather regular jet areas, which become perfectly circular in the limit in which all hard particles are separated in the plane by at least a distance , as can be seen in Fig. 1. Another important advantage of the anti- algorithm is that it has a very small back-reaction , that is, the presence of a soft background has reduced effects on which hard particles are clustered into a given jet.
The recent progress in jet algorithms can be summarized in Fig. 2. Each IRC unsafe cone jet algorithm can now be replaced by the corresponding IRC safe one, with a similar physics performance, shown in the last column of Fig. 2. SISCone is the natural IRC safe replacement for MidPoint-type iterative cone algorithms with split-merge (IC-SM), while anti- is so for iterative cone algorithms of the progressive removal (IC-PR) type .
This brief review is unable to cover many other interesting developements related to jets and jet finding in the recent years. Some of those not discussed here include the use of jet substructure as a useful technique to improve signal significance in various channels at the LHC (see for example [12, 13, 14]), analytical studies of the interplay between perturbative and non-perturbative effects in jet finding , the infrared safe definition of jet flavour and its application to precision predictions for jets at hadron colliders [16, 17] or the impact of jet measurements, both at the Tevatron and at HERA, in global analysis of PDFs [18, 19].
Performance of jet algorithms at LHC
A recurring question in jet studies is “what is the best jet definition for a given specific analysis”? Most existing techniques either use as a reference unphysical Monte Carlo partons (an ambiguous concept beyond LO) and/or assume some shape for the measured kinematical distributions. To overcome these disadvantages, a new strategy to quantify the performance of jet definitions in kinematic reconstruction tasks has been recently introduced , which is designed to make use exclusively of physical observables.
In Ref.  two quality measures respecting the above requirements are proposed, and applied to the kinematic reconstruction of invariant mass distributions in dijet events for a wide range of energies. These quality measures can in turn be mapped into an effective luminosity ratio, defined as
Given a certain signal significance with jet definition , indicates the factor more luminosity needed to obtain the same significance as with jet definition .
The results of  over a large range of jet definitions,111There results can also be accessed through an interactive web tool  which allows the user to compare the jet finding quality for a wide range of parameters (jet algorithm, , value of PU, …). summarized in Fig. 3, indicate that for gluon jets, and in general for TeV scales, there are significant benefits to be had from using larger radii that those commonly used, up to . In general, SISCone and C/A-filt (Cam/Aa supplemented with a filtering procedure ) show the best performance. These conclusions are robust in the presence of high-luminosity PU, when subtracted with the jet area technique .
Jet finding in AA collisions at RHIC and LHC
While QCD jets are ubiquitous in pp collisions, until this year no real jet reconstruction had been obtained in the much more challenging environment of HIC. Indeed, usually in HIC one refers to the leading particle of the event as a jet. However, reconstructing full QCD jets provides a much more precise window to the properties of the hot and dense medium created in the collision than just leading particles.
The difficulty in reconstructing jets in HIC stems from the huge backgrounds, which need to be subtracted in order to compare with baseline results. There are various techniques to subtract such large backgrounds. In  it was shown how the FastJet jet area method could efficiently subtract such backgrounds in HIC at the LHC with a good accuracy (see Fig. 4).
A major breakthrough in jet finding was the recent first measurement of QCD jets in HIC by the STAR collaboration at RHIC . In Fig. 4 we show their measurement with the algorithm. These results should have important consequences for understanding the medium properties in HIC.
It would be important, after these initial measurements, to improve the control on the accuracy of the subtraction procedure, as well as to understand the differences between the performances of different jet algorithms. Ongoing studies  suggest that one of the important sources of systematic error in the HIC jet reconstruction is back-reaction , therefore anti- is potentially interesting in this situation due to its small back-reaction . Ref.  also investigates how the use of local ranges for the determination of the background level might help reducing the effects of point-to-point background fluctuations. However, more work is still required in order to determine the optimal settings for jet finding in HIC.
Jet finding has seen a large number of important developements in the recent years, However, there is still room for more progress, which should be driven by the actual requirements of LHC data analysis. Jet finding will also be essential to exploit the heavy-ion program at the LHC as proved by the latest RHIC jet measurements.
This work has been supported by the grant ANR-05-JCJC-0046-01 (France). The author wants to acknowledge M. Cacciari, G. Salam and G. Soyez for help and material while preparing this review.
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