Study of ATLAS Jet Performance using Z' & ttbar
by Hai-Jun Yang (yhj@umich.edu) & Bing Zhou, University of Michigan, Ann Arbor

Physics Movitations (Ref: Paul Langacker, arXiv:0801.1345v2)

Among various proposed physics beyond the Standar Model (SM), additional U(1)' gauge symmetries and associated Z' gauge boson are one of the best motivated extensions of the SM, it would have profound implications for particle physics and cosmology. Implications of a Z' including an extended Higgs sector, extended neutralino sector and solution to the mu problem in supersymmetry; exotic fermions needed for anomaly cancellation; possible flavor changing neutral current effects; neutrino mass; possible Z' mediation of supersymmetry breaking; and cosmological implications for cold dark matter and electroweak baryogensis.
If there is a Z' with typical electroweak scale couplings to the ordinary fermions, it should be readily observable at the LHC for masses up to ~ 4 - 5 TeV, or at the Tevatron for masses up to ~ 600 - 900 GeV. Significant diagnostic probes of the Z' couplings would be possible up to 2 - 2.5 TeV. The latest results from CDF with 955 pb^-1 data ruled out topcolor leptophobic Z' below 720 GeV/c^2, and the cross section of Z'-like state decaying to ttbar is found to be less than 0.64 pb at 95% C.L. for M_Z' above 700 GeV/c^2 (Ref: T. Aaltonen et.al., PRD 77, 051102(R) (2008)).

With the increase of Z' mass and significantly high CM Energy at LHC (14 TeV proton-proton head on collision), the Top pairs from Z' decay will be highly boosted. It's a big challenge to reconstruct Top using b jet and W hadronic decay products (-> 2 jets) since they are largely overlapped. Apparently, large jet cone size (e.g. default value R = 0.7) is not suitable for Z' study simply because most of jets from highly boosted top decay are located in a relative small region. It is crucial to find suitable calorimeter clustering algorithms and jet finding algorithms to efficiently separate these hadronic jets and to well reconstruct W and Top.

Results and Conclusion:
Our studies of jet performance using Z' and ttbar MC events indicate that Kt4Jets algorithm yield the best results among eight available jet algorithms, as listed below.
- the highest reconstruction efficiency:
- Eff_W = 91%(Z'), 93%(ttbar)
- Eff_Top = 81.5%(Z'), 87.5%(ttbar)
- the closest reconstructed mass and the best W/Top mass resolution (RMS):
- M_W = 82.3 +/- 11.0(RMS) GeV for Z', 81.3 +/- 10.7(RMS) GeV for ttbar
- M_Top = 177.5 +/- 35.9(RMS) GeV for Z', 173.6 +/- 33.51(RMS) GeV for ttbar
Performace of ATLAS jet algorithms
Eight Jet Algorithms are Available for Analysis (Detailed descriptions are shown in the bottom)
- CJets(R=0.7)
- CTopoJets(R=0.7)
- C4Jets(R=0.4)
- C4TopoJets(R=0.4)
- Kt4Jets(R=0.4)
- Kt4TopoJets(R=0.4)
- Kt6Jets(R=0.6)
- Kt6TopoJets(R=0.6)
Monte Carlo Samples (V12)
- Dataset 6231, 5000 Events: Z' -> ttbar, M_Z' = 1 TeV, with one W^+ decays to e+ or mu+ with corresponding neutrino
- Dataset 5200, 5000 Events: ttbar with at least 1 lepton(e or mu) from W decays, 3967 out of 5000 events have one and only one W leptonic decay
Source Codes
Plots for Jet Multiplicity
Plots for W -> 2 Jets Reconstruction (with 40 < M_W < 120 GeV)
Plots for Top -> 3 Jets Reconstruction (with 50 < M_Top < 300 GeV)

W Efficiency Top Efficiency

ATLAS uses two principal calorimeter clustering algorithms (Ref: W. Lampl et.al., ATL-LARG-PUB-2008-002)
- "Sliding-window" algorithm, it clusters calorimeter cells within fixed-size rectangle window, the position of the window is adjusted so that its contained energy is a local maximum. It's efficient for reconstructing EM showers and jets from tau decay. The cluster size is fixed allows for a very precise cluster energy calibration.

- "Topological" algorithm, it starts with a seed cell and iterately adds neighboring cells to the cluster, as long as the signal in the cell is significant compared to noise(above threshold). It's efficient to suppress noise in clusters with large number of cells which is used for jet and MET reconstruction.

ATLAS uses two principal jet finding algorithms (Ref: S.D.Ellis & D.E.Soper, PRD 48 (1993) 3160)
- "Cone" algorithm, two protojets i and j are merged if each falls within an angular distance R of the merged jet axis (i+j->Jet). The limit on angular separation between the protojet and the merged Jet (including protojet i and j) has the simple formula: sqrt((phi_i - phi_Jet)**2 + (eta_i - eta_Jet)**2) < R. This processes is iterated until teh cone center matches the Jet center. The angular separation between two protojets dR = sqrt((phi_i - phi_j)**2 + (eta_i - eta_j)**2), R < dR < 2R. Thus it is possible with two equally energetic protojets located near opposite edges of the cone and nothing in the center of the cone. The cone jets always have well defined, smooth boundaries, although the amount of Et near the edge will depend on how the issue of the merging of overlapping jets is handled.
- "Kt" algorithm, it's a successive combination algorithm. The two protojets i and j with the smallest value of d_ij (=d_min) are merged if d_ij is less than the smaller of Et_i**2 and Et_j**2, where d_ij = min(Et_i**2, Et_j**2) * dR**2 / R**2, dR**2 = (phi_i - phi_j)**2 + (eta_i - eta_j)**2. If the smallest d_min is d_i(=Et_i**2), the protojet i is "not mergable", then remove it from the list of protojets and add it to the list of jets. The procedure continues until there are no more protojets. As it proceeds, it produces a list of jets with successively larger values of d_k = Et_k**2. To merge protojets i and j into a new protojet k with
Et_k = Et_i + Et_j, eta_k = (Et_i*eta_i + Et_j*eta_j )/Et_k, phi_k = (Et_i*phi_i + Et_j*phi_j )/Et_k
With the successive combination algorithm, the lower Et protojet can be far from the jet axis, up to a maximum separation R, while the higher Et protojet must be closer to the jet axis. Thus there is less transverse energy near the edge of the allowed angular region than that with the "Cone" algorithm.

Jets in Standard Reconstruction (Ref: Atlas Jet and MET Group)
Several jet collections are build during reconstruction, varying
- Input to jet finder : Calorimeter Tower, topological clusters or truth particles
- Jet Finder algorithm : Cone or Kt
- Main parameter of the jet finder
The collections are saved in ESD and AOD as JetCollection objects (in ESD) or ParticleJetContainer objects (in AOD).
A typical name (or key) for a JetCollection is 'Cone7H1TowerJets' and all names follow this pattern : (algorithm type)(main parameter)(calibration method)(input type)Jets.
More details on each aspects :
- Algorithm type
  - Cone : the seeded cone algorithm. Default parameters : Radius=0.4 or 0.7, Pt of seeds = 1 GeV, split/merge fraction=0.5
  - Kt : the inclusive kt algorithm (fast version), R parameter =0.4 or 0.6
- Main parameter : corresponds to Radius*10 for cone algs or R*10 for Kt algs.
- Input type
  - Towers : means calorimeter towers at EM scale
  - Topo : means topological clusters. If calibration type is H1, using clusters at EM scale. Else if calibration is LC, using calibrated TopoClusters
- calibration method
  - H1 : means the 'global' H1-style calibration is applied on jets after jet finding. The H1 calibration is specific for each type of jet finder and each value of the main parameter. For example, the set of corrections for Cone7H1TowerJets is different than for Cone7H1TopoJets and for Cone4H1TowerJets.
  - LC : means Local Calibration. It applies only to jets build from topo clusters. In this case the jet finder uses the local calibrated topoclusters (which include hadronic calibration, dead matrerial correction and after 13.0.1 out-of-cluster corrections).

-- Created by Hai-Jun Yang on May 6, 2008

Study of ATLAS Jet Performance using Z' & ttbar

Physics Movitations (Ref: Paul Langacker, arXiv:0801.1345v2)

Results and Conclusion:

Performace of ATLAS jet algorithms

ATLAS uses two principal calorimeter clustering algorithms (Ref: W. Lampl et.al., ATL-LARG-PUB-2008-002)

ATLAS uses two principal jet finding algorithms (Ref: S.D.Ellis & D.E.Soper, PRD 48 (1993) 3160)

Jets in Standard Reconstruction (Ref: Atlas Jet and MET Group)