Jet Finding Algorithm Research Articles

Jet overlap in heavy ion collisions at energies available at the CERN Large Hadron Collider and its consequences for the jet shape

Central lead-lead collisions at the LHC energies may pose a particular challenge for jet identification as multiple jets are produced per each collision event. We simulate the jet evolution in central Pb-Pb events at $\sqrt{s_{\rm NN}} = 2.76$ GeV collision energy with EPOS3 initial state, which typically contains multiple hard scatterings in each event. Therefore the partons from different jets have a significant chance to overlap in momentum space. We find that 30% of the jets with $p_\perp > 50$ GeV, identified by the standard anti-$k_\perp$ jet finding algorithm with jet cone size R=0.3, contain `intruder' particles from overlapping generator-level jets. This fraction increases with increasing beam energy and increasing R. The reconstructed momentum of the jet differs from that of the modelled jet by the loss due to jet partons which are outside of the jet cone and by the gain due to intruder partons. The sum of both may be positive or negative. These intruder partons particularly affect the radial jet momentum distribution because they contribute mostly at large angles $\Delta r$ with respect to the jet centre. The study stresses the importance of the jet overlap effect emerging in central lead-lead collisions at the LHC energies, while being negligible in peripheral PbPb or $p$Pb/$pp$ collisions.

Charged jet cross section and fragmentation in proton-proton collisions at s=7 TeV

We report the differential charged jet cross section and jet fragmentation distributions measured with the ALICE detector in proton-proton collisions at a centre-of-mass energy $\sqrt{s}=$ 7 TeV. Jets with pseudo-rapidity $\left| \eta \right| < {\rm 0.5}$ are reconstructed from charged particles using the anti-$k_{\rm T}$ jet finding algorithm with a resolution parameter $R$ = 0.4. The jet cross section is measured in the transverse momentum interval 5 $\leq p_{\rm T}^{\rm ch \; jet} <$ 100 GeV/$c$. Jet fragmentation is studied measuring the scaled transverse momentum spectra of the charged constituents of jets in four intervals of jet transverse momentum between 5 GeV/$c$ and 30 GeV/$c$. The measurements are compared to calculations from the PYTHIA model as well as next-to-leading order perturbative QCD calculations with POWHEG + PYTHIA8. The charged jet cross section is described by POWHEG for the entire measured range of $p_{\rm T}^{\rm ch \; jet}$. For $p_{\rm T}^{\rm ch \; jet}$ $>$ 40 GeV/$c$, the PYTHIA calculations also agree with the measured charged jet cross section. PYTHIA6 simulations describe the fragmentation distributions to 15%. Larger discrepancies are observed for PYTHIA8.

Performance studies of D-meson tagged jets in pp collisions at with ALICE

We present the current status of the measurement of jets that contain a D meson (D-tagged jets) with the ALICE detector. D0-meson candidates, identified via their hadronic decay into a Kπ pair, were combined with the other charged tracks reconstructed with the central tracking system, using the anti-kT jet-finding algorithm. The yield of D-tagged jets was extracted through an invariant mass analysis of the D-meson candidates. A Monte Carlo simulation was used to determine the detector performance and validate the signal extraction techniques.

J E T $$ {J}_{E_T} $$ : a global jet finding algorithm

We introduce a new jet-finding algorithm for a hadron collider based on maximizing a $$ {J}_{E_T} $$ function for all possible combinations of particles in an event. This function prefers a larger value of the jet transverse energy and a smaller value of the jet mass. The jet shape is proved to be a circular cone in Cartesian coordinates with the geometric center shifted from the jet momentum toward the central region. The jet cone size shrinks for a more forward jet. We have implemented our $$ {J}_{E_T} $$ algorithm with a reasonable running time scaling as Nn 3, where “N” is the total number of particles and “n” (≪N) is the number of particles in a fiducial region. Many features of our $$ {J}_{E_T} $$ jets are similar to anti-k t jets, including the reconstructed jet momentum and the “back-reaction” from soft contamination. Nevertheless, when the jet parameters in the two algorithms are matched using QCD jets, we find that the $$ {J}_{E_T} $$ algorithm has a larger efficiency than anti-k t for identifying objects with hard splittings such as a W-jet.

The dependence of Bose–Einstein correlations, on energy, multiplicity and hadronic jets

The dependence of the one-dimensional Bose–Einstein correlation R1D derived from proton–proton collisions is examined in terms of energy, hadron multiplicity and number of emerging hadronic jets. It is argued that the observed rise of R1D with energy is the result of the increase of the average number of hadronic jets. It is further shown that by the relatively straightforward measurements of R1D and its chaoticity parameter λ one should be able to estimate the average number of outgoing hadronic jets emitted over the entire final state phase space without the need to rely on a particular jet finding algorithm and its associated parameters.

The Influence of the Underlying Event on Jet Measurements in Heavy Ion Collisions

We present a study of the performance of jet reconstruction algorithms for Pb+Pb collisions at = 5.52 TeV based on a full GEANT simulation of the ATLAS detector. It is shown that ATLAS can provide measurements that are sensitive to different in-medium energy loss scenarios leading to the jet quenching. The capability of measurements of fragmentation function and jT distribution are presented. We concentrate on some biases in these measurements that might be due to the detector effects or to the choice of a jet finding algorithm.

Exploring Jet Properties in p-p Collisions at 200 GeV with STAR

The mechanisms underlying hadronization are not well understood, both in vacuum and in hot QCD matter. Precise characterization of jet fragmentation to hadrons in p-p collisions will help elucidate the fundamental process of hadronization, and will serve as essential reference to measure the modification of hadronization in heavy ion collisions. We present measurements of fragmentation functions for unidentified particles in jets produced in p-p collisions at 200 GeV using the STAR detector at RHIC. The results from different jet reconstruction algorithms are compared, including variations of the resolution parameter. It is found that the results are largely insensitive to details of the jet-finding algorithm at RHIC energies. Particle production inside and outside of these reconstructed jets will be compared to improve our understanding of the hadronization mechanisms for soft and hard particles in p-p events at RHIC energies.

A cone jet-finding algorithm for heavy-ion collisions at LHC energies

Standard jet-finding techniques used in elementary particle collisions have not been successful in the high track density of heavy-ion collisions. This paper describes a modified cone-type jet-finding algorithm developed for the complex environment of heavy-ion collisions. The primary modification to the algorithm is the evaluation and subtraction of the large background energy, arising from uncorrelated soft hadrons, in each collision. A detailed analysis of the background energy and its event-by-event fluctuations has been performed on simulated data, and a method developed to estimate the background energy inside the jet cone from the measured energy outside the cone on an event-by-event basis. The algorithm has been tested using Monte Carlo simulations of Pb+Pb collisions at for the ALICE detector at the LHC. The algorithm can reconstruct jets with a transverse energy of 50 GeV and above with an energy resolution of ∼30%.

Optimal Jet Finder (v1.0 C++)

We describe a C++ implementation of the Optimal Jet Definition for identification of jets in hadronic final states of particle collisions. We explain interface subroutines and provide a usage example. The source code is available from http://www.inr.ac.ru/~ftkachov/projects/jets/. Program summary Title of program: Optimal Jet Finder (v1.0 C++) Catalogue identifier: ADSB_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADSB_v2_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer: any computer with a standard C++ compiler Tested with: (1) GNU gcc 3.4.2, Linux Fedora Core 3, Intel i686; (2) Forte Developer 7 C++ 5.4, SunOS 5.9, UltraSPARC III+; (3) Microsoft Visual C++ Toolkit 2003 (compiler 13.10.3077, linker 7.10.30777, option /EHsc), Windows XP, Intel i686. Programming language used: C++ Memory required: ∼ 1 MB (or more, depending on the settings) No. of lines in distributed program, including test data, etc.: 3047 No. of bytes in distributed program, including test data, etc.: 17 884 Distribution format: tar.gz Nature of physical problem: Analysis of hadronic final states in high energy particle collision experiments often involves identification of hadronic jets. A large number of hadrons detected in the calorimeter is reduced to a few jets by means of a jet finding algorithm. The jets are used in further analysis which would be difficult or impossible when applied directly to the hadrons. Grigoriev et al. [D.Yu. Grigoriev, E. Jankowski, F.V. Tkachov, Phys. Rev. Lett. 91 (2003) 061801] provide brief introduction to the subject of jet finding algorithms and a general review of the physics of jets can be found in [R. Barlow, Rep. Prog. Phys. 36 (1993) 1067]. Method of solution: The software we provide is an implementation of the so-called Optimal Jet Definition (OJD). The theory of OJD was developed in [F.V. Tkachov, Phys. Rev. Lett. 73 (1994) 2405; Erratum, Phys. Rev. Lett. 74 (1995) 2618; F.V. Tkachov, Int. J. Modern Phys. A 12 (1997) 5411; F.V. Tkachov, Int. J. Modern Phys. A 17 (2002) 2783]. The desired jet configuration is obtained as the one that minimizes Ω, a certain function of the input particles and jet configuration. A FORTRAN 77 implementation of OJD is described in [D.Yu. Grigoriev, E. Jankowski, F.V. Tkachov, Comput. Phys. Comm. 155 (2003) 42]. Restrictions on the complexity of the program: Memory required by the program is proportional to the number of particles in the input × the number of jets in the output. For example, for 650 particles and 20 jets ∼ 300 KB memory is required. Typical running time: The running time (in the running mode with a fixed number of jets) is proportional to the number of particles in the input × the number of jets in the output × times the number of different random initial configurations tried ( ntries). For example, for 65 particles in the input and 4 jets in the output, the running time is ∼ 4 ⋅ 10 −3 s per try (Pentium 4 2.8 GHz).

Optimal Jet Finder

We describe a FORTRAN 77 implementation of the optimal jet definition for identification of jets in hadronic final states of particle collisions. We discuss details of the implementation, explain interface subroutines and provide a usage example. The source code is available from http://www.inr.ac.ru/~ftkachov/projects/jets/. Program summary Title of program: Optimal Jet Finder (OJF_014) Catalogue identifier: ADSB Program Summary URL: http://cpc.cs.qub.ac.uk/summaries/ADSB Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer: Any computer with the FORTRAN 77 compiler Tested with: g77/Linux on Intel, Alpha and Sparc; Sun f77/Solaris (thwgs.cern.ch); xlf/AIX (rsplus.cern.ch); MS Fortran PowerStation 4.0/Win98 Programming language used: FORTRAN 77 Memory required: ∼1 MB (or more, depending on the settings) Number of bytes in distributed program, including examples and test data: 251 463 Distribution format: tar gzip file Keywords: Hadronic jets, jet finding algorithms Nature of physical problem: Analysis of hadronic final states in high energy particle collision experiments often involves identification of hadronic jets. A large number of hadrons detected in the calorimeter is reduced to a few jets by means of a jet finding algorithm. The jets are used in further analysis which would be difficult or impossible when applied directly to the hadrons. Grigoriev et al. [ hep-ph/0301185] provide a brief introduction to the subject of jet finding algorithms and a general review of the physics of jets can be found in [Rep. Prog. Phys. 36 (1993) 1067]. Method of solution: The software we provide is an implementation of the so-called optimal jet definition ( OJD). The theory of OJD was developed by Tkachov [Phys. Rev. Lett. 73 (1994) 2405; 74 (1995) 2618; Int. J. Mod. Phys. A 12 (1997) 5411; 17 (2002) 2783]. The desired jet configuration is obtained as the one that minimizes Ω R , a certain function of the input particles and jet configuration. Restrictions on the complexity of the program: The size of the largest data structure the program uses is (maximal number of particles in the input) × (maximal number of jets in the output) × 8 bytes. (For the standard settings <1 MB). Therefore, there is no memory restriction for any conceivable application for which the program was designed. Typical running time: The running time depends strongly on the physical process being analyzed and the parameters used. For the benchmark process we studied, e + e −→ W + W −→ 4 jets , with the average number of ∼80 particles in the input, the running time was <10 −2 s on a modest PC (per event with n tries=1). For a fixed number of jets the complexity of the algorithm grows linearly with the number of particles (cells) in the input, in contrast with other known jet finding algorithms for which this dependence is cubic. The reader is referred to Grigoriev et al. [ hep-ph/0301185] for a more detailed discussion of this issue.

Production of D ∗ mesons in photon-photon collisions at √ see = 183 GeV and 189 GeV using the OPAL detector at LEP

The inclusive production of D ∗± mesons in photon-photon collisions has been measured using the OPAL detector at LEP at e +e − centre-of-mass energies √ s ee of 183 and 189 GeV. The D ∗+ mesons are reconstructed in their decay to D 0 π + with the D 0 observed in the two decay modes K − π + and K − π + π − π +. After background subtraction, 121 ± 14 (stat.) D ∗± events have been selected. Jets are reconstructed using a cone jet finding algorithm to separate direct and single-resolved events. Differential cross-sections dσ/ dp T D ∗ and dσ/ dvbη D ∗ vb as functions of the D ∗± transverse momentum p T D ∗ and pseudorapidity η D ∗ are presented in the kinematic region 2 < p T D ∗ < 12 GeV and vbη D ∗ vb < 1.5 . They are compared to next-to-leading order (NLO) perturbative QCD calculations. The total cross-section for the process e +e − → e +e −c c in the anti-tagged mode is measured to be σ (e +e − → e +e −c c ) = (945 ± 239) pb with a direct contribution of σ (e +e − → e +e −c c ) dir = (392 ± 117) pb and a single-resolved contribution of σ (e +e − → e +e −c c ) res = (553 ± 184) pb.

Di-Jet production in photon-photon collisions at $\sqrt{s}_{\rm ee}=161$ and 172 GeV

Di-jet production is studied in collisions of quasi-real photons radiated by the LEP beams at e\(^+\)e\(^-\) centre-of-mass energies \(\sqrt{s}_{\rm ee}=161\) and 172 GeV. The jets are reconstructed using a cone jet finding algorithm. The angular distributions of direct and double-resolved processes are measured and compared to the predictions of leading order and next-to-leading order perturbative QCD. The jet energy profiles are also studied. The inclusive di-jet cross-section is measured as a function of \(E_{\rm T}^{\rm jet}\) and \(|\eta^{\rm jet}|\) and compared to next-to-leading order perturbative QCD calculations. The inclusive di-jet cross-section as a function of \(|\eta^{\rm jet}|\) is compared to the prediction of the leading order Monte Carlo generators PYTHIA and PHOJET. The Monte Carlo predictions are calculated with different parametrisations of the parton distributions of the photon. The influence of the ‘underlying event’ has been studied to reduce the model dependence of the predicted jet cross-sections from the Monte Carlo generators.

Measurement of the jet width in γγ collisions and in e+e− annihilation process at TRISTAN

The shape of jets produced in (quasi-) real photon-photon collisions as well as in e + e − annihilation process has been studied with a cone jet finding algorithm, using the data taken with the TOPAZ detector at the TRISTAN e + e − collider at an average center-of-mass energy ( s ee ) of 58 GeV. The results are presented in terms of the jet width as a function of the jet transverse energy ( E T jet) as well as a scaled transverse jet energy, x T (=2 E T jet / s ). The jet width narrows as E jet T increases; however, at the same value of E T jet the jet width in γγ collisions at TRISTAN is significantly narrower than that in γp collisions at HERA. By comparing our results with the data in other reactions, it has been shown that the jet width in γγ, γp, p p ̄ collisions as well as the e + e − annihilation process has an approximate scaling behavior as a function of x T .

Production of

The production of ${\rm K}^0_{\rm S}$ mesons and $\Lambda$ baryons in quark and gluon jets has been investigated using two complementary techniques. In the first approach, which provides high statistical accuracy, jets were selected using different jet finding algorithms and ordered according to their energy. Production rates were determined taking into account the dependences of quark and gluon compositions as a function of jet energy as predicted by Monte Carlo models. Selecting three-jet events with the $k_{\perp}$ (Durham) jet finder ( $y_{\mathrm{cut}} = 0.005$ ), the ratios of ${\rm K}^0_{\rm S}$ and $\Lambda$ production rates in gluon and quark jets relative to the mean charged particle multiplicity were found to be $1.10 \pm 0.02 \pm 0.02$ and $1.41 \pm 0.04 \pm 0.04$ , respectively, where the first uncertainty is statistical and the second is systematic. In the second approach, a new method of identifying quark jets based on the collimation of energy flow around the jet axis is introduced and was used to anti-tag gluon jets in symmetric (Y-shaped) three-jet events. Using the cone jet finding algorithm with a cone size of 30°, the ratios of relative production rates in gluon and quark jets were determined to be $0.94 \pm 0.07 \pm 0.07$ for $\mathrm{K^0_S}$ and $1.18 \pm 0.10 \pm 0.17$ for $\Lambda$ . The results of both analyses are compared to the predictions of Monte Carlo models.

Di-Jet production in photon-photon collisions at

Di-jet production is studied in collisions of quasi-real photons radiated by the LEP beams at e(-)e(-) centre-of-mass energies root s(ee) = 161 and 172 GeV. The jets are reconstructed using a cone jet finding algorithm. The angular distributions of direct and double-resolved processes are measured and compared to the predictions of leading order and nest-to-leading order perturbative QCD. The jet energy profiles are also studied. The inclusive di-jet cross-section is measured as a function of E-T(jet) and \eta(jet) and compared to next-to-leading order perturbative QCD calculations. The inclusive di-jet cross-section as a function of \eta(jet) is compared to the prediction of the leading order Monte Carlo generators PYTHIA and PHOJET. The Monte Carlo predictions are calculated with different parametrisations of the parton distributions of the photon. The influence of the 'underlying event' has been studied to reduce the model dependence of the predicted jet cross-sections from the Monte Carlo generators.

Multiplicity distributions of gluon and quark jets and a test of QCD analytic calculations

Gluon jets are identified in e +e − hadronic annihilation events by tagging two quark jets in the same hemisphere of an event. The gluon jet is defined inclusively as all the particles in the opposite hemisphere. Gluon hets defined in this manner have a close correspondence to gluon jets as they are defined for analytic calculations, and are almost independent of a jet finding algorithm. The mean and first few higher moments of the gluon jet charged particle multiplicity distribution are compared to the analogous results found for light quark (uds) jets, also defined inclusively. Large differences are observed between the mean, skew and curtosis values of the gluon and quark jets, but not between their dispersions. The cumulant factorial moments of the distributions are also measured, and are used to test the predictions of QCD analytic calculations. A calculation which includes next-to-next-to-leading order corrections and energy conservation is observed to provide a much improved description of the separated gluon and quark jet cumulant moments compared to a next-to-leading order calculation without energy conservation. There is good quantitative agreement between the data and calculations for the ratios of the cumulant moments between gluon and quark jets. The data sample used is the LEP-1 sample of the OPAL experiment at LEP.

Production of ${\rm K}^0_{\rm S}$ and $\Lambda$ in quark and gluon jets from $\mathrm{Z^0}$ decay

The production of \({\rm K}^0_{\rm S}\) mesons and \(\Lambda\) baryons in quark and gluon jets has been investigated using two complementary techniques. In the first approach, which provides high statistical accuracy, jets were selected using different jet finding algorithms and ordered according to their energy. Production rates were determined taking into account the dependences of quark and gluon compositions as a function of jet energy as predicted by Monte Carlo models. Selecting three-jet events with the \(k_{\perp}\) (Durham) jet finder (\(y_{\mathrm{cut}} = 0.005\)), the ratios of \({\rm K}^0_{\rm S}\) and \(\Lambda\) production rates in gluon and quark jets relative to the mean charged particle multiplicity were found to be \(1.10 \pm 0.02 \pm 0.02\) and \(1.41 \pm 0.04 \pm 0.04\), respectively, where the first uncertainty is statistical and the second is systematic. In the second approach, a new method of identifying quark jets based on the collimation of energy flow around the jet axis is introduced and was used to anti-tag gluon jets in symmetric (Y-shaped) three-jet events. Using the cone jet finding algorithm with a cone size of 30°, the ratios of relative production rates in gluon and quark jets were determined to be \(0.94 \pm 0.07 \pm 0.07\) for \(\mathrm{K^0_S}\) and \(1.18 \pm 0.10 \pm 0.17\) for \(\Lambda\). The results of both analyses are compared to the predictions of Monte Carlo models.

Multiplicity distributions of gluon and quark jets and tests of QCD analytic predictions

Gluon jets are identified in ${\rm e^+e^-}$ hadronic annihilation events by tagging two quark jets in the same hemisphere of an event. The gluon jet is defined inclusively as all the particles in the opposite hemisphere. Gluon jets defined in this manner have a close correspondence to gluon jets as they are defined for analytic calculations, and are almost independent of a jet finding algorithm. The charged particle multiplicity distribution of the gluon jets is presented, and is analyzed for its mean, dispersion, skew, and curtosis values, and for its factorial and cumulant moments. The results are compared to the analogous results found for a sample of light quark (uds) jets, also defined inclusively. We observe differences between the mean, skew and curtosis values of gluon and quark jets, but not between their dispersions. The cumulant moment results are compared to the predictions of QCD analytic calculations. A calculation which includes next-to-next-to-leading order corrections and energy conservation is observed to provide a much improved description of the data compared to a next-to-leading order calculation without energy conservation. There is agreement between the data and calculations for the ratios of the cumulant moments between gluon and quark jets.

Algorithmic bias on observed hadronic jet properties

The biases introduced by the widely used geometric (‘cone’) jet—finding algorithms are investigated using a simple Monte—Carlo program in which the only free parameters are the multiplicity of calorimeter clusters and their average energy. The jet profiles, jet multiplicities and jet widths produced from the simulation are compared to those using real data. A jet finding algorithm which searches for a correlated jet signal is also examined.

Cone algorithm jets ine+e−collisions

The structure of hadronic jets depends not only on the dynamics of QCD but also on the details of the jet finding algorithm and the physical process in which the jet is produced. To study these effects in more detail we calculate the jet cross section and the internal jet structure in ${e}^{+}{e}^{\ensuremath{-}}$ annihilations and compare them to the results found in hadronic collisions using the same jet definition, the cone algorithm. The different structures of the overall events in the two cases are evident in the comparison. For a given cone size and jet energy, the distribution of energy inside the cone is more concentrated near the center for jets from ${e}^{+}{e}^{\ensuremath{-}}$ collisions than for jets from hadronic collisions.