a.zinchenko, g.chabratova jinr, dubna. russia

A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad

Chambers and its Development for the Forward Muon Spectrometer of ALICE

A.Zinchenko, G.Chabratova

JINR, Dubna. Russia

VIII INTERNATIONAL WORKSHOP ON ADVANCED COMPUTING AND ANALYSIS TECHNIQUES IN

PHYSICS RESEARCH (ACAT'2002)24-28 June, 2002, Moscow, Russia

A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the

Forward Muon Spectrometer of ALICE

A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia

Overview The ALICE Experiment & MUON Spectrometer

Physical Tasks & Requirements to MUON Tracking

Basic Ideas of Bayesian Unfolding

Application to MUON Cluster Finding

Results & Discussion

Conclusion

General overview of Muon Spectrometer


A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward

Muon Spectrometer of ALICE




(1S) (2S) (3S)

Mass (MeV) 9460.37±0.21 10023.3±0.31 10355.3±0.5

Difference 560 MeV 330 MeV





Requirement to the tracking and reconstruction efficiency: mass resolution has to be < 100 MeV

Requirement to the detector response reconstruction: a reconstruction algorithm has to reduce the statistical noise and does not introduce excessive smothing.


Bayer' theorem: G.D. Agostini NIM A362(1995)487 If anybody observes a single event E(effect), the probability that it has been due to the i th cause of Ci, i=1,2,..,nc is proportional to the probability of cause P(Ci) times the probability of the cause to produce the effect P(E|Ci).




Basic Ideas of Bayesian Unfolding

in

iii

iii

CPCEP

CPCEPECP

1

)()|(

)()|()|(



An application to the positron emission tomography. Pairs of photons are registered in coincidence by pairs of detectors. The region, where the image is reconstructed is subdivided into pixels and different pairs of detectors. Since the number of emissions inside pixels and number of of photon coincidences are described by the Poisson statistics, the likelihood function can be written

Basic Ideas of Bayesian Unfolding (cont) Maximum Likelihoods - Expectation Maximization (MLEM):

L.A. Shepp and Y. Vard IEEE Trans.Med.Im.v.1(1982)113


!)(

,...,1

,...,1 ij

nij

nj

ni neL

ijp

t

ij



where -vector of pixel activities , - the mean number of emissions from the pixel j

contributing to the tube i, is the number of photon pairs counted in the tube i from the pixel j.

is the number of detectors , - number of pixels. The Expectation step of the EM algorithm is done by taking a conditional expectation of log likelihood with a respect of parameter estimates

at the nth iteration and measured counts The new value for the jth component of the vector

where - the jth pixel visibility from the detector i. The results of reconstruction is shown at picture.

),...,( 1 pn


Basic Ideas of Bayesian Unfolding (cont)

n i n j

n

cij

n ij

ij

j

iji nn

ik

n

kij

iij

iij

njn

j cnc

c

1



Detector: Cathod Pad Chamber (CPC). Sizes of pads vary from (0.4x0.6)cm2 to (10.x0.7143)cm2

Old method: The pad charge distribution is described by two-dimensional integral of the Mathieson function and coordinates of a single track is extracted from the fit of pad charge distributed by this function. The number of track candidates is estimated from the number of local maxima in the pad charge distribution. An amount of events with significant overlapping of signal and background induced pad charges is not negligible. An estimation of the number of track candidates from the local maxima is not sufficiency accurate and results in deterioration of coordinate resolution.





New method:transform the "two-cathode fixed pad size" problem into the "one-anode plane variable pixel size" one. Find a groups of adjacent pads on

one cathode and overlap with its pads on the other cathode precluster

Precluster array of pixels in the anode plane with size defined by the overlap of pads on both cathodes.

It is assumed that each pixel contains a track





New method(cont):Iterative procedure: Track j has an initial value of energy release . Usually all 's are set to 1.

with

where - the expected signal on pad i with track energy releases at the kth iteration, - the track-to-pad coupling(signal on pad i from track j given by Mathieson) and - the number of tracks in the array.

ki

iN

iijN

iij

kjk

j fqc

c

pp

pads

pads

1

1

1

Application to MUON Cluster Finding(cont)

p j0

p j0

f ik

p jk

cijN track


trsckN

j

kiij

ki pcf

1



New method (cont): after several iterations (10-15) the pixel size is decreased by two; track candidates with the lowest energy releases are removed, if the total number of candidates exceeds the number of pads; interactive procedure is repeated;Algorithm stops when the pixel size becomes sufficiently small (1mm)

Application to MUON Cluster Finding(cont)





Results: residuals in the non bending plane




Results(cont): residuals in the bending plane




Conclusion:

New method of Cluster Finding and Hit Reconstruction improves essentially the space resolution of CPC chambers for the Forward Muon Spectrometer of ALICE

a.zinchenko, g.chabratova jinr, dubna. russia

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