Jet reconstruction with Deterministic Annealing

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Jet reconstruction with Deterministic Annealing

• Davide Perrino
• Dipartimento di Fisica INFN di Bari
• Terzo Convegno Nazionale sulla Fisica di Alice
  13/11/2007

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Deterministic Annealing

• Its a general purpose algorithm customized for
  jet finding in hadronic collisions
• Clustering consists of gathering n initial data
  xi in a set of k codevectors yj that represent
  the sample depending on its elements closeness
• Clustering is achieved through the minimization
  of a cost function D under a constrain (T )

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Deterministic Annealing
The distance determines how will the algorithm
work. A squared cone distance was chosen
Clustering takes place by means of the
minimization of a cost function so defined
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Deterministic Annealing
To avoid a trivial solution it is necessary the
introduction of an entropy term
The minimization of D corresponds to look for the
minimum of the function under the constrain of a
multiplier T
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Deterministic Annealing
The procedure is deterministic since for every
T are optimized the values of
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Deterministic Annealing
b0
b0.0049
b0.0056
b0.0100
b0.0156
b0.0347
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Advantages of DA

• The algorithm is naturally infrared and
  collinear safe.
• CPU time depends on Na with 1ltalt1.5, depending on
  the method used.
• Independent of detector segmentation (no grid
  needed).
• It needs no further patches procedures
  (merging, splitting etc.)
• Few parameters needed only to smooth the
  clusterization process gt they dont affect the
  physical result.
• Only two procedures needed 1) to decide when to
  stop the clusterization and 2) to select which
  clusters are jets.

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Background subtraction and jets selection
Evaluate clusters energy density
Start with clusters list
Recalculate background
Start with jets list
Calculate mean ?(Etbg) and rms
Is Et gt Etbgrms
Subtract background
y
Add cluster to jet list
n
Store jets
Is clusters list exausted?
n
y
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Events settings
The analysis was performed on the same sets of
events generated for cone and kT studies. (taken
from Rafael)
Pythia 6.2 (p-p Jets)
Centre mass energy 5.5 TeV Process types
MSEL Structure Function
CTEQ5L Initial/final state radiation On Multiple
interactions Off Jet quenching
Off parton pt hard range 45-150 GeV/c
65-150
95-500
150-1000
200-1000
HIJING 1.36 (Pb-Pb Underlying event)
vsNN 5.5 TeV jet
quenching On Nuclear effects
on PDF On Initial/final state radiation On
Resonance decays Off Jet trigger
Off Impact Parameter
0 5 fm
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Events study

• Find jets in Pythia events with
• hlt2
• no cut on Pt
• no cut on charge

• Use jets found in the most populated bin as a
  trigger for jets found in PythiaHijing events
  with
• hlt.9
• Ptgt2. GeV/c
• Cuts on particles
• no cut on charge
• cut on charge (w/o FastSimTPC)

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Events study
Example of input jets selection for 50 GeV sample.
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Jet reconstruction efficiency
Were selected jets that satisfied Dhlt0.5 Dflt0.5
Efficiency improves with jet energy in all the
cases.
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Energy ratio
Energy ratio between Et reconstructed and energy
input. It remains almost constant w.r.t. input Et.
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Energy resolution
Energy resolution with charged particles and with
fast simulation are similar to those obtained
through the cone analysis.
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Direction resolution
As one can expext, it improves considerably with
jet energy in all the cases.
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Conclusions

• DA has been adapted to jet finding in pp and
  Pb-Pb events.
• DA owns many interesting features for jet
  finding.
• An analysis on five sets of PythiaHijing events
  corresponding to different ranges of jet energies
  has been performed, adding a fast TPC simulation.
• An event-by-event background subtraction method
  has been implemented for DA.