A Study on Cluster Resolution

1
A Study on Cluster Resolution

• Neighborhood hit density gradients are proposed
  as a means for
• -- identifying cluster boundaries
• -- implementing a cluster split/merge strategy
• Relies on the inspection of calorimeter
  domains collections of
• connected cells ganged as projective towers.
  Currently coded in
• box form ? ( n x m x l ) cells as segmented
  in (theta,phi,layer).
• A tool to be used as a sup-
• port to clustering algorithms.
• Equally applicable to both
• analogue and digital readouts.

neighborhood hit density gradients
?1
?2
A. Maciel (NIU), Simulation E-flow Wshop , NIU,
November 7-9, 2002
2
Cluster ID Calorimeter Domain Methods

Gmax

• EM shower profiles suggest pre-clustering
• box of 4x4 cells.
• Locate (4 x 4 x all) domain with highest
• energy (or hits).
• Inspect neighborhood w/ grads i.e. find
• (Rmin, Gmin) and (Rmax,Gmax).
• If Gmax gt kGmin, then a secondary cluster
• is declared found (currently using k 2 ).
• Rmin Rmax determine a search area for
• next-hottest (4 x 4 x all) domain.
• Cross check that ?2 cluster also sees ?1
• Use both sets of RG(min,max) to re-size
  clusters.

Gmin
Rmin
Rmax

search area for ?2


?1
Rmin1
Rmax size
A. Maciel (NIU), Simulation E-flow Wshop , NIU,
November 7-9, 2002
3
p0 ( 10GeV ) ? ? ? 5K single-p0 events
? ? distance, generated (cm)
1 layers 0 -- 9 2 layers 10--19
neighborhood 2 is tested if neighborhood 1 fails
1 cell 0.5 cm
? ? distance, reconstructed (of cells)
5000 events superimposed
(of cells)
A. Maciel (NIU), Simulation E-flow Wshop , NIU,
November 7-9, 2002
4
Generated (upper) .vs. Reconstructed (lower)
GeV
inefficiency
A. Maciel (NIU), Simulation E-flow Wshop , NIU,
November 7-9, 2002
5
Domain (Projective Box) Energy Resolution
A. Maciel (NIU), Simulation E-flow Wshop , NIU,
November 7-9, 2002
6
Layer energy centroid position fluctuations
across layers (distances in cell units)
?1 pre-cluster
?1 re-sized
?2 pre-cluster
?2 re-sized
A. Maciel (NIU), Simulation E-flow Wshop , NIU,
November 7-9, 2002
7
A series of event displays for 10GeV p0 ?
? ? with the associated neighborhood
gradients analysis as an illustration of the
method.
8
Example of a symmetric decay
Evt 81 Gamma1 ThetaBin420 PhiBin213
Reco Energy 4.87 MC Energy 5.28 Gamma2
ThetaBin417 PhiBin204 Reco Energy
4.39 MC Energy 4.72
Event 81
Neighborhood Grads
9
?1 looks at ?2 layers used 0--9
distance, in number of cells
?2 looks at ?1 layers used 0--9
distance, in number of cells
Event 81
10
Example of an asymmetric decay Evt 36 Rmin1 4
, Rmax1 9 Rmin2 36, Rmax2 9 , DeltaR
10 Gamma1 ThetaBin420 PhiBin288
Box-Reco Energy8.09 ( MC 8.88 ) Gamma2
ThetaBin410 PhiBin289 Box-Reco
Energy1.33 ( MC 1.12 )
Event 36
Neighborhood Grads
11
?1 looks at ?2 layers used 0--9
distance, in number of cells
?2 looks at ?1 layers used 0--9
distance, in number of cells
Event 36
12
Evt 48 (how it can get tricky...) Gamma1
Energy8.10 MC 9.50 Gamma2 Energy0.31
MC 0.50
dirt
?2
?1
Event 48
Neighborhood Grads
13
Note Grads search was cylindrical (as opposed
to directional, in theta and phi)
?1 looks at ?2 layers used 0--9
?1
?2
dirt
distance, in number of cells
?2 looks at ?1 layers used 0--9
?1
?2
dirt
distance, in number of cells
Event 48
14
Evt 184 ( A case of extreme asymmetry )
Gamma1 ThetaBin419 PhiBin1603
Reco Energy9.45 MC Energy 9.98 Gamma2
ThetaBin414 PhiBin1588 Reco
Energy0.050 MC Energy0.021
Event 184
Neighborhood Grads
15
layers 1019
Rmin1 10 , Rmax1 13 hsize1 13 , DeltaR 15
layers 09 cannot detect gamma_2
?2
()
layers 09
layers 2029
?1
?2
Event 184
() clearly, any level of noise here turns this
into an inefficiency...
16
Evt 284 (Gamma_2 is a late shower)
Gamma1 ThetaBin419 PhiBin1492 Reco
Energy7.91 MC Energy8.04 Gamma2
ThetaBin417 PhiBin1483 Reco
Energy2.15 MC Energy1.96
Event 284
Neighborhood Grads
17
layers 1019
?1
?1
?2
Rmin1 4 Rmax1 7 hsize1 5
layers 09 cannot detect gamma_2
?2
?1
layers 09
Rmin2 4 Rmax2 8 DeltaR 9
layers 2029
?1
?2
Event 284
18
EM Shower Characteristics in the SD Detector
Model

• The next two slides display shower profiles for
  electrons and gammas respectively
• Profiles are averaged over samples of 5000
  monochromatic single particles (10GeV)
• All plots are longitudinal profiles, where the
  x-axis labels the layer number
• -- Energy deposition per layer -- Layer hosting
  hottest cell
• -- Number of hits per layer -- Layer mean
  square radius ()

() definition
A. Maciel (NIU), Simulation E-flow Wshop , NIU,
November 7-9, 2002
19
SD 10GeV single ?s in Em-Cal (5k evts.)
GeV
shower-max
n.of cells
hit-max
energy-weighted transverse shower radius (in of
cells)
A. Maciel (NIU), Simulation E-flow Wshop , NIU,
November 7-9, 2002