-- AlexanderFedotov - 18-Oct-2010

Jet Algorithms

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FastJet algoritms employed in CMSSW

In CMSSW, the jet finding is interfaced to the FastJet package. The employed FastJet algorithms are ( details ):

  • SISCone ( SISConePlugin )
  • IterativeCone ( CMSIterativeConePlugin )
  • CDFMidPoint ( CDFMidPointPlugin )
  • ATLASCone ( ATLASConePlugin )
  • Kt ( JetDefinition(fastjet::kt_algorithm,...) )
  • CambridgeAachen ( JetDefinition (fastjet::antikt_algorithm,...) )
  • AntiKt ( JetDefinition (fastjet::genkt_algorithm,...) )
  • GeneralizedKt ( JetDefinition(fastjet::genkt_algorithm,...) )

CMS Iterative Cone algorithm

FastJet manual

The FastJet manual gives very liitle info on the algoritm in the Section 7.3.5 CMS iterative cone :

"The (iterative) cone (with progressive removal) algorithm used by CMS during the preparation for the LHC.

#include ‘‘fastjet/CMSIterativeConePlugin.hh’’
///...
CMSIterativeConePlugin (double ConeRadius, double SeedThreshold=0.0);
The underlying code for this algorithm was extracted from the CMSSW web site, with certain small service routines having been rewritten by the FastJet authors. The resulting code was validated by clustering 1000 events with the original version of the CMS software and comparing the output to the clustering performed with the FastJet plugin. The jet contents were identical in all cases. However the jet momenta differed at a relative precision level of , related to the use of singleprecision arithmetic at some internal stage of the CMS software (while the FastJet version is in double precision).

Note: this algorithm is unsafe [6] . It is to be deprecated for new experimental or theoretical analyses.

. . .

[6] M. Cacciari, G. P. Salam and G. Soyez, JHEP 0804 (2008) 063 [arXiv:0802.1189 [hep-ph ]] (pdf) .

"

CMS PTDR1

An Iterative Cone description is available in the Section 11.2: Jet algorithms of the CMS Physics TDR Vol.I .

Reproduced below is a structured html version of this document (the sub-chapter 11.2), containing, along with the iterative cone description, also a description of a midpoint and an inclusive algorithms.

PTDR1: 11.2 Jet algorithms

The first jet algorithms for hadron physics were simple cones [ 250 , 259 ]. Over the last two decades, clustering techniques have greatly improved in sophistication. Three principal jet reconstruction algorithms have been coded and studied for CMS:

  • the iterative cone [260],
  • the midpoint cone [261] and
  • the inclusive jet algorithm [ 262, 263 ].
The midpoint-cone and algorithms are widely used in offline analysis in current hadron collider experiments, while the iterative cone algorithm is simpler and faster and commonly used for jet reconstruction in software-based trigger systems.

The jet algorithms may be used with one of two recombination schemes for adding the constituents.

  • In the energy scheme , constituents are simply added as four-vectors. This produces massive jets .
  • In the scheme , massless jets are produced
    • by equating the jet transverse momentum to the of the constituents and then
    • fixing the direction of the jet in one of two ways:
      1. where is the jet energy (usually used with cone algorithms), or
      2. and (usually used with the algorithm).
    • In all cases the jet is equal to .

The inclusive algorithm merges, in each iteration step, input objects into possible final jets and so the new jet quantities, the jet direction and energy, have to be calculated directly during the clustering. The cone jet algorithms, iterative and midpoint, group the input objects together as an intermediate stage and the final determination of the jet quantities (recombination) is done in one step at the end of the jet finding.

PTDR1: 11.2.1 Iterative cone

In the iterative cone algorithm, an -ordered list of input objects (particles or calorimeter towers) is created.

  • A cone of size in space is cast around the input object having the largest transverse energy above a specified seed threshold.
    • The objects inside the cone are used to calculate a “proto-jet” direction and energy using the scheme.
      • The computed direction is used to seed a new proto-jet.
      • The procedure is repeated until the energy of the proto-jet changes by less than 1% between iterations and the direction of the proto-jet changes by .
    • When a stable proto-jet is found, all objects in the proto-jet are removed from the list of input objects and the stable proto-jet is added to the list of jets.
  • The whole procedure is repeated until the list contains no more objects with an above the seed threshold.

The cone size and the seed threshold are parameters of the algorithm.

When the algorithm is terminated, a different recombination scheme may be applied to jet constituents to define the final jet kinematic properties.

PTDR1: 11.2.2 Midpoint cone

The midpont-cone algorithm was designed to facilitate the splitting and merging of jets.

The midpoint-cone algorithm also uses an iterative procedure to find stable cones (proto-jets) starting from the cones around objects with an above a seed threshold.

In contrast to the iterative cone algorithm described above, no object is removed from the input list. This can result in overlapping proto-jets (a single input object may belong to several proto-jets).

To ensure the collinear and infrared safety of the algorithm, a second iteration of the list of stable jets is done. For every pair of proto-jets that are closer than the cone diameter, a midpoint is calculated as the direction of the combined momentum. These midpoints are then used as additional seeds to find more proto-jets.

When all proto-jets are found,

  • the splitting and merging procedure is applied, starting with the highest proto-jet.
    • If the proto-jet does not share objects with other proto-jets, it is defined as a jet and removed from the proto-jet list.
    • Otherwise, the transverse energy shared with the highest neighbor proto-jet is compared to the total transverse energy of this neighbor proto-jet.
      • If the fraction is greater than (typically 50%) the proto-jets are merged,
      • otherwise the shared objects are individually assigned to the proto-jet that is closest in space.
  • The procedure is repeated, again always starting with the highest proto-jet, until no proto-jets are left.

This algorithm implements the energy scheme to calculate the proto-jet properties but a different recombination scheme may be used for the final jet.

The parameters of the algorithm include

  • a seed threshold,
  • a cone radius,
  • a threshold on the shared energy fraction for jet merging,
  • and also a maximum number of proto-jets that are used to calculate midpoints.

PTDR1: Inclusive algorithm

The inclusive jet algorithm is a cluster-based jet algorithm.

  • The cluster procedure starts with a list of input objects, stable particles or calorimeter cells.
  • For each object and each pair the following distances are calculated:
    where is a dimensionless parameter normally set to unity [ 261 ].
  • The algorithm searches for the smallest or .
    • If a value of type is the smallest, the corresponding objects and are removed from the list of input objects.
      They are merged using one of the recombination schemes listed below (AF: above? ) and filled as one new object into the list of input objects.
    • If a distance of type is the smallest, then the corresponding object is removed from the list of input objects and filled into the list of final jets.
  • The procedure is repeated until all objects are included in jets.

The algorithm successively merges objects which have a distance .

It follows that for all final jets and .

PTDR1: References

[250] C. Bromberg et al., “Observation of the Production of Jets of Particles at High Transverse Momentum and Comparison with Inclusive Single Particle Reactions,” Phys. Rev. Lett. 38 (1977) 1447. doi:10.1103/PhysRevLett.38.1447 .
[259] UA1 Collaboration, G. Arnison et al., “Hadronic Jet Production at the CERN Proton - Anti-Proton Collider,” Phys. Lett. B132 (1983) 214. doi:10.1016/0370-2693(83)90254-X .
[260] S. V. Chekanov, “Jet algorithms: A mini review,” arXiv:hep-ph/0211298 .
[261] G. C. Blazey et al., “Run II jet physics,” arXiv:hep-ex/0005012 .
[262] J. M. Butterworth, J. P. Couchman, B. E. Cox, and B. M.Waugh, “KtJet: A C++ implementation of the K(T) clustering algorithm,” Comput. Phys. Commun. 153 (2003)85–96, arXiv:hep-ph/0210022 . doi:10.1016/S0010-4655(03)00156-5 .
[263] S. D. Ellis and D. E. Soper, “Successive combination jet algorithm for hadron collisions,” Phys. Rev. D48 (1993) 3160–3166, arXiv:hep-ph/9305266 . doi:10.1103/PhysRevD.48.3160 .


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Topic revision: r5 - 2010-10-19 - AlexanderFedotov
 
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