Review on recent developements in jet finding

Review on recent developements in jet finding

Juan Rojo
Abstract

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


Juan Rojo

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 [3] 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 [6]. These fast implementations are available through the FastJet package [7], 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 [8]. 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 [8], 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 [9]. 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 [10].

Another recently developed IRC safe jet algorithm is the anti- algorithm [11]. 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 [9], 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 [1].

Fig. 1: Jet areas for the (left) and anti- (right) algorithms for .
Fig. 2: Summary of the progress in jet algorithms since 2005.

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 [15], 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 [20], which is designed to make use exclusively of physical observables.

In Ref. [20] 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

(1)

Given a certain signal significance with jet definition , indicates the factor more luminosity needed to obtain the same significance as with jet definition .

Fig. 3:

The effective luminosity ratio, Eq. 1, for quark and gluon jets at 100 GeV and 2 TeV [20].

The results of [20] over a large range of jet definitions,111There results can also be accessed through an interactive web tool [21] 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 [12]) show the best performance. These conclusions are robust in the presence of high-luminosity PU, when subtracted with the jet area technique [10].

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 [10] 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 [22]. 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 [23] suggest that one of the important sources of systematic error in the HIC jet reconstruction is back-reaction [9], therefore anti- is potentially interesting in this situation due to its small back-reaction [11]. Ref. [23] 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.

Fig. 4:

Outlook

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.

Acknowledgments

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.

References

  • [1] C. Buttar et al. (2008). 0803.0678 [hep-ph]
  • [2] S. D. Ellis, J. Huston, K. Hatakeyama, P. Loch, and M. Tonnesmann, Prog. Part. Nucl. Phys. 60, 484 (2008). 0712.2447
  • [3] S. Catani, Y. L. Dokshitzer, M. H. Seymour, and B. R. Webber, Nucl. Phys. B406, 187 (1993)
  • [4] S. Catani, Y. L. Dokshitzer, M. Olsson, G. Turnock, and B. R. Webber, Phys. Lett. B269, 432 (1991)
  • [5] M. Wobisch and T. Wengler (1998). hep-ph/9907280
  • [6] M. Cacciari and G. P. Salam, Phys. Lett. B641, 57 (2006). hep-ph/0512210
  • [7] M. Cacciari, G. P. Salam, and G. Soyez (2005-2008). http://www.lpthe.jussieu.fr/salam/fastjet
  • [8] G. P. Salam and G. Soyez, JHEP 05, 086 (2007). 0704.0292 [hep-ph]
  • [9] M. Cacciari, G. P. Salam, and G. Soyez, JHEP 04, 005 (2008). 0802.1188
  • [10] M. Cacciari and G. P. Salam, Phys. Lett. B659, 119 (2008). 0707.1378
  • [11] M. Cacciari, G. P. Salam, and G. Soyez, JHEP 04, 063 (2008). 0802.1189
  • [12] J. M. Butterworth, A. R. Davison, M. Rubin, and G. P. Salam, Phys. Rev. Lett. 100, 242001 (2008). 0802.2470
  • [13] D. E. Kaplan, K. Rehermann, M. D. Schwartz, and B. Tweedie, Phys. Rev. Lett. 101, 142001 (2008). 0806.0848
  • [14] J. Thaler and L.-T. Wang, JHEP 07, 092 (2008). 0806.0023
  • [15] M. Dasgupta, L. Magnea, and G. P. Salam, JHEP 02, 055 (2008). 0712.3014
  • [16] A. Banfi, G. P. Salam, and G. Zanderighi, Eur. Phys. J. C47, 113 (2006). hep-ph/0601139
  • [17] A. Banfi, G. P. Salam, and G. Zanderighi, JHEP 07, 026 (2007). 0704.2999
  • [18] NNPDF Collaboration, R. D. Ball et al. (2008). 0808.1231
  • [19] P. M. Nadolsky et al., Phys. Rev. D78, 013004 (2008). 0802.0007
  • [20] M. Cacciari, J. Rojo, G. P. Salam, and G. Soyez (2008). 0810.1304
  • [21] M. Cacciari, J. Rojo, G. P. Salam, and G. Soyez (2008), http://quality.fastjet.fr/
  • [22] STAR Collaboration, S. Salur (2008). 0809.1609
  • [23] M. Cacciari, J. Rojo, G. P. Salam, and G. Soyez , in preparation.
Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
290039
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description