Muon track reconstruction in the CSC detector by yurtgc548

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									Cluster Quality in Track Fitting for
     the ATLAS CSC Detector
                             IEEE - NSS
                      San Diego, 30 October 2006



David Primor1, Nir Amram1, Erez Etzion1, Giora Mikenberg2, Hagit Messer1
                       1. Tel Aviv University – Israel
                 2. Weizmann Institute of Science - Israel


                                                                           1
                                  Outline
•   The CSC local tracking problem
•   The algorithms approach
•   The use of cluster quality
•   Fitting comparison
•   Conclusions




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        The ATLAS detector
 The Muon spectrometer
  The CSC detector




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                       The CSC signals
   The maximum charge
   distribution over the strips:


                                                                               2.54 mm

                                                  5.08 mm




     The signal shape in time
     for a single strip:


                                                                                         [ns]


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                          Muon tracks




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  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
          Input: Raw Data


                      Activity detection
Stage 1


                      within time interval




                             Track finding

                   Output/Input: Rough tracks
Stage 2




           Cluster finding and parameter estimation



                            Line fitting



                          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 1   . The
  clean cluster has a position error distribution ~ N (0,  0 )
                                                             2


  The dirty one has a position error distribution~ N (0,  12 )

• We chose:                     0  100  m

                                1  10 0
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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:
                                                                            In time + mask hit
    • Contains “mask” strips or
    • not well separated from other clusters or
    • does not Follow the Matheison distribution.

                                                                                             [x 25 ns]

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


                         pD dirty  pD clean  a




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




                   About third of the muon clusters are “dirty”


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Calculating the quality – The model
                                         Spatial signal Matheison shape
                                                                                      noise

    The Model:                     y (n)  AS x ( n; x p )  r (n)
                                                Amplitude
                                                                       Hit position


   The ML:                          ˆ ˆ
                                  ( A, x p )  arg min | Y  C( x p ) A |2
                                                             A, x p




Y  [ y(0), y(1),.. y( N )]

C( xp )  [S (0  xp ), S (1  xp ),..., S ( N 1  xp )]T

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                  Calculating the quality
                                                                (YT C( x p )) 2
       The solution:                    x p  arg max
                                        ˆ
                                                      xp       C( x p )T C( x p )




         The quality:                                        (YT C( x p )) 2
                                       Q  arg max                   T
                                                                                
                                                xp         C( x p ) C( x p )




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                       Quality of clusters




                                                   Possible
                                                   threshold
                                                   value




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               Different fitting methods
1.     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:
                                     1
                                     2         clean hits
                                     0
                                  w
                                     1          dirty hits
                                      12
                                    
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.



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Simulation results for different layer number


                                                                                  Good
                                                                                  probability

                                                                                   0.75
Residual
between
real and
estimated
track
                                                                                  Quality prob.

                                                                                    a  0.8
                                   Number of layers




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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)


                                                                                 Number of layers = 8
Residual
between                                                                              a 1
real and
estimated
track




                                                   1 


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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

Residual
between                                                                      Number of layers = 8
real and
estimated
track




                                                  a

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     Discussion- detection probability
1.    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 finding efficiency
                                                                      Restricted
                                                                                   1

                                                         Robust                    0.95
                                          WLS
                       Iterative LS
               LS
                                                                                   0.9

                                                                                   0.85

                                                                                   0.8

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


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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



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