We review recent developments related to jet clustering algorithms and jet
reconstruction, with particular emphasis on their implications in heavy ion
collisions. These developments 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
show how jet reconstruction provides a useful tool to probe the characteristics
of the hot and dense medium created in heavy ion collisions, which allows one
to distinguish between different models of parton-medium interaction.Comment: 7 pages, 4 figures, to appear in the proceedings of the 13th
  International Conference on Elastic & Diffractive Scattering, CERN, 29th June
  - 3rd July 200

Rojo, Juan

English

arXiv

We review recent developments related to jet clustering algorithms and jet reconstruction, with particular emphasis on their implications in heavy ion collisions. These developments 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 show how jet reconstruction provides a useful tool to probe the characteristics of the hot and dense medium created in heavy ion collisions, which allows one to distinguish between different models of parton-medium interaction

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Progress in Jet Reconstruction in Heavy IonCollisionsJuan RojoINFN, Sezione di Milano, Via Celoria 16, I - 20133, Milano (Italy)We review recent developments related to jet clustering algorithms and jet reconstruction,with particular emphasis on their implications in heavy ion collisions. These developmentsinclude fast implementations of sequential recombination algorithms, new IRC safe algo-rithms, quantitative determination of jet areas and quality measures for jet finding, amongmany others. We also show how jet reconstruction provides a useful tool to probe thecharacteristics of the hot and dense medium created in heavy ion collisions, which allowsto distinguish between different models of parton-medium interaction.1 Recent Developments in Jet AlgorithmsWith the upcoming start-up of the proton-proton and heavy ion programs at the LHC, jetreconstruction techniques have been the subject of intense research in the recent years [1, 2, 3, 4].In this contribution we briefly review this progress with special emphasis on their implicationsin heavy ion collisions.An important development has been the fast implementation of the kT [5] and Cam-bridge/Aachen [6, 7] jet algorithms. Prior to 2005, existing implementations scaled as N 3,with N the number of particles to be clustered, thus making it unpractical for high multiplicityproton-proton collisions, and even more in heavy ion collisions (HIC). Thanks to computationalgeometry methods, the performance of these algorithms was made to scale as N ln N [8]. Thesefast implementations are available through the FastJet package [9], together with area-basedsubtraction methods and plugins to external jet finders.Another important achievement has been the formulation of a practical (scaling as N 2 ln N)infrared and collinear (IRC) safe cone algorithm, SISCone [10]. Unlike all other commonly usedcone algorithms, SISCone is IRC safe to all orders in perturbation theory by construction. Thisproperty allows one to compare any perturbative computation with experimental data, whichfor IRC unsafe algorithms is impossible beyond some fixed order [10]. The phenomenologicalimplications of SISCone when compared with the (IRC unsafe) commonly used MidPoint conealgorithm range from few percent differences in the inclusive jet spectrum, somewhat largerin the presence of realistic Underlying Event (UE), up to 50% differences for more exclusiveobservables, 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, speciallysince the naive jet area is ambiguous beyond LO. The situation was recently clarified by theintroduction of quantitative definitions of jet areas based on the catchment properties of hardjets with respect to very soft particles, called ghosts in [11]. On top of their theoretical im-portance, jet areas have important applications related to the subtraction of soft backgrounds359coming from the UE or from Pile-Up (PU), both in proton-proton and in heavy-ion collisions,as discussed in [12].Another recently developed IRC safe jet algorithm is the anti-kt algorithm [13]. This al-gorithm is related to kT and Cam/Aa by its distance measure, dij ≡ min(k2pti , k2ptj )∆R2ij/R2,with p = −1 (p = 1 corresponds to kT and p = 0 to Cam/Aa). The anti-kT algorithm has theproperty of being soft-resilient, that is, due to its distance soft particles are always clusteredwith hard particles first. This property leads to rather regular jet areas, which become perfectlycircular in the limit in which all hard particles are separated in the (y, φ) plane by at least adistance R [13]. Another important advantage of the anti-kt algorithm is that it has a verysmall back-reaction, that is, the presence of a soft background has reduced effects on whichhard particles are clustered into a given jet. This is a particularly relevant advantage of theanti-kt algorithm for jet reconstruction in very dense environments like heavy ion collisions.2 Performance of Jet AlgorithmsA recurring question in jet studies is “what is the best jet definition for a given specific analysisunder certain experimental conditions”? Most existing techniques either use as a referenceunphysical Monte Carlo partons (an ambiguous concept beyond LO) and/or assume some shapefor the measured kinematic distributions. To overcome these disadvantages, a new strategy toquantify the performance of jet definitions in kinematic reconstruction tasks has been recentlyintroduced [14], which was designed to make use exclusively of physical observables. Relatedanalytical studies which address the same question were discussed in Ref. [15].In Ref. [14] two quality measures respecting the above requirements are proposed, and ap-plied to the kinematic reconstruction of invariant mass distributions in dijet events in simulatedLHC proton-proton collisions for a wide range of energies. These quality measures can in turnbe mapped into an effective luminosity ratio, defined asρL(JD2/JD1) ≡ L(needed with JD2)L(needed with JD1) =[Σ (JD1)Σ (JD2)]2. (1)Given a certain signal significance Σ with jet definition JD2, ρL(JD2/JD1) indicates the factormore luminosity needed to obtain the same significance as with jet definition JD1.The results of [14] over a large range of jet definitions,1 summarised in Fig.. 1, indicate thatfor gluon jets, and in general for TeV scales, there are significant benefits to be had from usinglarger radii that those commonly used, up to R & 1. In general, SISCone and C/A-filt (Cam/Aasupplemented with a filtering procedure [17]) show the best performance. These conclusions arerobust in the presence of high-luminosity PU, when subtracted with the jet area technique [12].The same techniques could be applied to heavy ion collisions to determine how in such case theoptimal jet definition is affected by the overwhelming underlying event present.3 Jet Reconstruction in Heavy Ion CollisionsWhile QCD jets are ubiquitous in pp collisions, until recently [18, 19] no real jet reconstructionhad been obtained in the much more challenging environment of HIC. Indeed, usually in HIC1There results can also be accessed through an interactive web tool [16] which allows the user to comparethe jet finding quality for a wide range of parameters (jet algorithm, R, value of PU, ...).J ROJO360Figure 1: The effective luminosity ratio, Eq. 1, for quark and gluon jets at 100 GeV and 2 TeV, fromRef. [14].one refers to the leading particle of the event as a jet. However, reconstructing full QCD jetsprovides a much more precise window to the properties of the hot and dense medium createdin the collision than just leading particles.The difficulty in reconstructing jets in HIC stems from the huge backgrounds, which needto be subtracted in order to compare with baseline results, like proton-proton or proton-ioncollisions at the same energy. There are various techniques to subtract such large backgrounds.In Ref. [12] it was shown how the area method introduced above could efficiently subtract largeUE backgrounds in HIC for LHC conditions with good accuracy, see Fig. 2.It is therefore important for precision measurements to control the accuracy of the subtrac-tion procedure intrinsic to jet reconstruction in HIC, as well as to understand the differencesbetween the performances of different jet algorithms. Ongoing studies [20] suggest that oneof the dominant sources of systematic error in HIC jet reconstruction is back-reaction [11],therefore anti-kt is potentially interesting in this situation due to its small back-reaction [13].In Ref. [20] also the use of local ranges for the determination of the background level ρ as atechnique to reduced the effects of point-to-point background fluctuations is investigated.Related to progress in jet reconstruction algorithms, an important development in the recentyears has been the development of several exclusive Monte Carlo event generators for heavyion collisions which account for the interaction of partons propagating within the hot anddense medium created in the collision [21, 22, 23, 24]. These event generators, which assumedifferent models for the parton-medium interaction [25], can be used together with modern jetreconstruction techniques in order to determine, under realistic experimental conditions, whichjet-related observables are at the same time more robust and more sensitive to the differentPROGRESS IN JET RECONSTRUCTION IN HEAVY ION COLLISIONS36110-610-510-410-310-210-1100101102103-50  0  50  100  150  2001/n coll d n jets / d Pt [GeV-1 ]Pt [GeV]LHC, Pb Pb, √s = 5.5 TeVHydjet, dNch/dy = 1600|y| < 5scaled ppraw Pb-PbPb-Pb with subtractionkt, R=0.4Figure 2: The simulated inclusive jet spectrum at the LHC with the kT algorithm, including subtrac-tion, from Ref. [12].scenarios for the hot and dense medium dynamics.As an illustration of how these Monte Carlo programs with medium effects can be coupledto jet reconstruction techniques and be used to determine medium properties in HIC, in Fig. 3we show preliminary results for two observables which are sensitive to medium effects: the dijetazimuthal correlations and the jet shape. Jet shapes are defined analogously to [21]. To obtainthese results, hard events with pT ≥ 100 GeV are generated and then propagated through amodel of the hot medium by means of the Q-PYTHIA Monte Carlo [21], for different values ofthe medium parameters. The resulting hadronic event is embedded into a minimum bias PbPbevent generated with the PSM Monte Carlo [26] for different scenarios of central multiplicityat the LHC. Jet reconstruction is performed with different algorithms of the FastJet package,and UE subtraction is performed with the jet area method. In the particular examples of Fig. 3the jet radius is chosen to be R = 0.5.For the two examples of Fig. 3, we show the proton-proton baseline results with and withoutparton-medium interactions, whose strength is characterised by the parameter qˆL [21], with Lthe medium length. The medium effects are clearly visible for the two observables, inducing abroadening of the jet shape and a decorrelation of the dijet azimuthal spectrum. These curves,with no HIC UE, are labelled as ’No PbPb’. Then we also show the corresponding results whenthe pp event is embedded into the PbPb event, in which case the UE event has been subtractedwith the area method. These curves are labelled as ’PbPb, subtraction’. We observe how afterthe background subtraction the baseline proton-proton results are reasonably recovered, in bothcases with (qˆL 6= 0) and without (qˆL = 0) medium effects.These preliminary results indicate that medium-sensitive jet related observables can beaccurately reconstructed even in the presence of large backgrounds, and are thus useful probesof the details of the parton-medium interactions. More work however is required to quantifythe accuracy with which the hot and dense medium created in HIC, and the values of theparameters which characterise it, can be studied by reconstructed jets and related observables.J ROJO362 [rad]dijetφ ∆2.5 2.6 2.7 2.8 2.9 3 3.1dijetφ∆/ddijetσ ddijetσ1/0.511.522.533.5Dijet azimuthal correlationspp -> gg=100 GeVT,minp=5.5 TeV, NSHPbPb at sqrt{s}Cam/Aa(filt), R=0.5qhL = 0, no PbPbqhL = 0, with PbPbqhL = 0, with PbPb, subtractionqhL = 20 GeV, no PbPbqhL = 20 GeV, with PbPbqhL = 20 GeV, with PbPb, subtractionj/Rsjr = R0.3 0.4 0.5 0.6 0.7 0.8 0.9 1>j T(r)/psj T(r) = <pφ0.50.60.70.80.91Jet shapepp -> gg=100 GeVT,jetpPbPb @ 5.5 TeV (NSH) alg, R=0.5TAnti-KqhL = 0, no PbPbqhL = 0, w PbPb, subqhL = 20 GeV, no PbPbqhL = 20 GeV, w PbPb, subFigure 3: Preliminary results for full jet reconstruction, including background subtraction, of jet-related observables under realistic experimental conditions at the LHC: dijet azimuthal correlations(upper plot) and jet shapes (lower plot). See text for details.PROGRESS IN JET RECONSTRUCTION IN HEAVY ION COLLISIONS363AcknowledgementsThe author wants to acknowledge M. Cacciari, G. Salam and G. Soyez for collaboration in thisresearch, as well as N. Armesto and C. Salgado for assistance with Q-PYTHIA.References[1] S. D. Ellis, J. Huston, K. Hatakeyama, P. Loch, and M. Tonnesmann. Jets in Hadron-Hadron Collisions.Prog. Part. Nucl. Phys., 60:484–551, 2008.[2] C. Buttar et al. Standard Model Handles and Candles Working Group: Tools and Jets Summary Report.2008.[3] Gavin P. Salam. Towards Jetography. 2009.[4] Matteo Cacciari. Recent Progress in Jet Algorithms and Their Impact in Underlying Event Studies. 2009.[5] S. Catani, Yuri L. Dokshitzer, M. H. Seymour, and B. R. Webber. Longitudinally invariant kt clusteringalgorithms for hadron hadron collisions. Nucl. Phys., B406:187–224, 1993.[6] S. Catani, Yuri L. Dokshitzer, M. Olsson, G. Turnock, and B. R. Webber. New clustering algorithm formulti - jet cross-sections in e+e− annihilation. Phys. Lett., B269:432–438, 1991.[7] M. Wobisch and T. Wengler. Hadronization corrections to jet cross sections in deep- inelastic scattering.1998.[8] Matteo Cacciari and Gavin P. Salam. Dispelling the N3 myth for the kt jet-finder. Phys. Lett., B641:57–61,2006.[9] Matteo Cacciari, Gavin P. Salam, and Gregory Soyez. 2005-2009.[10] Gavin P. Salam and Gregory Soyez. A practical seedless infrared-safe cone jet algorithm. JHEP, 05:086,2007.[11] Matteo Cacciari, Gavin P. Salam, and Gregory Soyez. The Catchment Area of Jets. JHEP, 04:005, 2008.[12] Matteo Cacciari and Gavin P. Salam. Pileup subtraction using jet areas. Phys. Lett., B659:119–126, 2008.[13] Matteo Cacciari, Gavin P. Salam, and Gregory Soyez. The anti-kt jet clustering algorithm. JHEP, 04:063,2008.[14] Matteo Cacciari, Juan Rojo, Gavin P. Salam, and Gregory Soyez. Quantifying the performance of jetdefinitions for kinematic reconstruction at the LHC. JHEP, 12:032, 2008.[15] Mrinal Dasgupta, Lorenzo Magnea, and Gavin P. Salam. Non-perturbative QCD effects in jets at hadroncolliders. JHEP, 02:055, 2008.[16] Matteo Cacciari, Juan Rojo, Gavin P. Salam, and Gregory Soyez. 2008.[17] Jonathan M. Butterworth, Adam R. Davison, Mathieu Rubin, and Gavin P. Salam. Jet substructure as anew Higgs search channel at the LHC. Phys. Rev. Lett., 100:242001, 2008.[18] Yue-Shi Lai. Probing medium-induced energy loss with direct jet reconstruction in p+p and Cu+Cucollisions at PHENIX. 2009.[19] Sevil Salur. Full Jet Reconstruction in Heavy Ion Collisions. 2009.[20] Matteo Cacciari, Juan Rojo, Gavin P. Salam, and Gregory Soyez. Quantifying the performance of jetdefinitions and subtraction in HIC at the LHC. in preparation.[21] Nestor Armesto, Leticia Cunqueiro, and Carlos A. Salgado. Q-PYTHIA: a medium-modified implementa-tion of final state radiation. 2009.[22] Korinna Zapp, Gunnar Ingelman, Johan Rathsman, Johanna Stachel, and Urs Achim Wiedemann. AMonte Carlo Model for ’Jet Quenching’. Eur. Phys. J., C60:617–632, 2009.[23] I. P. Lokhtin et al. Heavy ion event generator HYDJET++ (HYDrodynamics plus JETs). Comput. Phys.Commun., 180:779–799, 2009.[24] Nestor Armesto, Gennaro Corcella, Leticia Cunqueiro, and Carlos A. Salgado. Angular-ordered partonshowers with medium-modified splitting functions. 2009.[25] Carlos A. Salgado. Lectures on high-energy heavy-ion collisions at the LHC. 2009.[26] N. S. Amelin, N. Armesto, C. Pajares, and D. Sousa. Monte Carlo model for nuclear collisions from SPSto LHC energies. Eur. Phys. J., C22:149–163, 2001.J ROJO364

Progress in jet reconstruction and heavy ion collisions

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