1. 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

2. 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

3. 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

4. General overview of Muon Spectrometer A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward Muon Spectrometer of ALICE

5. A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia  (1S)  (2S)  (3S) Mass (MeV) 9460.37±0.21 10023.3±0.31 10355.3±0.5 Difference 560 MeV 330 MeV Physical Tasks & Requirements to MUON Tracking

6. A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward Muon Spectrometer of ALICE Physical Tasks & Requirements to MUON Tracking 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. A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia

7. 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 C i, i=1,2,..,n c is proportional to the probability of cause P(C i ) times the probability of the cause to produce the effect P(E|C i ). 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 Basic Ideas of Bayesian Unfolding

8. A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward Muon Spectrometer of ALICE 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 A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia

9. A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward Muon Spectrometer of ALICE 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 n th iteration and measured counts The new value for the j th component of the vector where - the jth pixel visibility from the detector i. The results of reconstruction is shown at picture. A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia Basic Ideas of Bayesian Unfolding (cont)

10. A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward Muon Spectrometer of ALICE Detector: Cathod Pad Chamber (CPC). Sizes of pads vary from (0.4x0.6)cm 2 to (10.x0.7143)cm 2 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. A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia Application to MUON Cluster Finding

11. A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward Muon Spectrometer of ALICE ¥ 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 A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia Application to MUON Cluster Finding

12. A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward Muon Spectrometer of ALICE 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 k th iteration, - the track-to-pad coupling(signal on pad i from track j given by Mathieson) and - the number of tracks in the array. Application to MUON Cluster Finding(cont) A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia

13. A New Approach to Cluster Finding and Hit Reconstruction in Cathode Pad Chambers and its Development for the Forward Muon Spectrometer of ALICE 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) A.Zinchenko, G.Chabratova ACAT 2002, Moscow, 24-28 June, 2002, Russia

15. 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 Results: residuals in the non bending plane

16. 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 Results(cont): residuals in the bending plane

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