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Cluster Quality in Track Fitting for the ATLAS CSC Detector

David Primor1, Nir Amram1, Erez Etzion1, Giora Mikenberg2, Hagit Messer1

1. Tel Aviv University – Israel2. Weizmann Institute of Science - Israel

IEEE - NSS San Diego, 30 October 2006

IEEE-NSS, 30.10.2006E. Etzion, Cluster Quality for tracking at ATLAS

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Outline

• The CSC local tracking problem• The algorithms approach• The use of cluster quality• Fitting comparison• Conclusions

IEEE-NSS, 30.10.2006E. Etzion, Cluster Quality for tracking at ATLAS

CSC3

The ATLAS detectorThe Muon spectrometerThe CSC detector

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CSC 4

The CSC signalsThe maximum charge distribution over the strips:

The signal shape in time for a single strip:

[ns]

2.54 mm

5.08 mm

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E. Etzion, Cluster Quality for tracking at ATLAS CSC

Muon tracks

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CSC

Muon tracks in a presence of high radiation background

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The tracking problem

•Estimating the number of tracks

•Estimating the hits positions

•Associating hits and tracks

•Estimating the track parameters

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The detect-before-estimate approach

Activity detection within time interval

Track finding

Line fitting

Cluster finding and parameter estimation

Sta

ge 1

Sta

ge 2

Input: Raw Data

Output/Input: Rough tracks

Output: Fine tracks

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MWPC and fitting techniques

• In order to study the possible contribution of the hit clusters quality, we simulate general MWPC detector.

• Discuss the benefits of using the quality and compare different fitting techniques.

• Utilize the ATLAS CSC line fitting to demonstrate the cluster quality ideas.

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The simulation

• The simulation produced muon tracks with random parameters (5000 events)

• The muon leaves a cluster of hits in each layer it crosses.• There are two types of hit clusters: clean clusters with

probability and dirty ones with probability . The clean cluster has a position error distribution The dirty one has a position error distribution

• We chose:

1 2

0~ (0, )N 2

1~ (0, )N

0 100 m

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Calculating the cluster quality

A “clean” cluster is:

• Contains only “in time” strips.

• Well separated from other clusters.

• Follow the Matheison distribution.

A “dirty” cluster is:

• Contains “mask” strips or

• not well separated from other clusters or

• does not Follow the Matheison distribution.

E. Etzion, Cluster Quality for tracking at ATLAS CSC

In time + mask hit

[x 25 ns]

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Equal detection probability

• We assume that the probabilities of dirty and clean hit detection are identical:

dirty cleanD Dp p a

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Dirty clusters rate

About third of the muon clusters are “dirty”

From test beam data (about 3KHz/cm2 radiation background)

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Calculating the quality – The model

)();()( nrxnASny px

Spatial signal Matheison shape noise

AmplitudeHit position

[ (0), (1),.. ( )]y y y NY

( ) [ (0 ), (1 ),..., ( 1 )]Tp p p px S x S x S N x C

The Model:

2

,

ˆ ˆ( , ) arg min | ( ) |p

p pA x

A x x A Y CThe ML:

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Calculating the quality2( ( ))

ˆ arg max( ) ( )p

Tp

p Tx p p

xx

x x

Y C

C CThe solution:

2( ( ))arg max

( ) ( )p

Tp

Tx p p

xQ

x x

Y C

C CThe quality:

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Quality of clusters

Possible threshold value

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Different fitting methods1. Least Squares (LS) – all points are used with equal weights in the track fitting

process.2. WLS – the “dirty” clusters gets reduced weight than the “clean” clusters,

according to the optimal solution:

3. Robust fitting – iterative procedure which recalculate the weights according to the residual between the hits and the estimated track.

4. Iterative LS – omitting the point with the higher residual in each iteration.5. Restricted LS – taking only the “clean” clusters.

20

21

1clean hits

1dirty hits

w

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Simulation results for different layer number

0.75

0.8a

Number of layers

Residual between real and estimated track

E. Etzion, Cluster Quality for tracking at ATLAS CSC

Good probability

Quality prob.

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Discussion- number of detection layers

1. The use of the hit quality improves the fitting results.2. Good fitting results, in a presence of radiation background, can be achieved

using more then 7 layers. If the number of layers is less then 6, the performance is reduced.

3. The iterative and Robust fitting techniques improve the LS fitting results when the number of layers is greater than 5.

4. The ATLAS CSC has only 4 layers…

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Simulation results for different contamination level (radiation background)

1

1a Residual between real and estimated track

Number of layers = 8

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Discussion- radiation background level

1. The use of the hit quality improves the fitting results.2. There is no significant performance difference for results of contamination

factor between 0 to 30%, when the fitting techniques use the hit quality (WLS, Robust+WLS, Restricted).

3. The performance of the algorithms that use the hit quality is similar.4. The LS fitting technique gets the worst results.

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Simulation results for different probability of detection

0.75

a

Residual between real and estimated track

Number of layers = 8

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Discussion- detection probability1. The use of the hit quality improves the fitting results.2. The probability of detection affect only the techniques that use the hit quality.3. If the detection probability is lower then 0.8 the fitting performance is reduced

significantly.

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Fitting results for Test Beam data with photon interference source:

Track fitting efficiency – less then 5 sigma (of the chamber resolution) from the real track

Track f inding eff iciency

RobustWLS

Iterative LSLS

Restricted

0.8

0.85

0.9

0.95

1

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Discussion - CSC The track fitting can be significantly improved using the cluster

quality based on time shape and the likelihood to the ideal Matheison shape.

The restricted method gets the best results (using only the clean clusters).

Where there are less than two clean cluster for a track candidate, it is not possible to produce high quality track. The clean cluster should be used, however, in the overall muon spectrometer track fitting.

While the CSC has only 4 layers. Depending on the background level of the LHC, larger number of layers could improve tracking efficiency

E. Etzion, Cluster Quality for tracking at ATLAS CSC