1. Pattern recognition with the triplet method Fabrizio Cei INFN & University of Pisa MEG Meeting, Hakata 22-23 October 2013 23/10/20131 Fabrizio Cei

2. Outline 23/10/2013 2  Algorithm strategy  Limitations & Inefficiencies  Results on GEM4 pure signal tracks  Results on GEM4 signal tracks mixed with Michel background (bartender, 400 ns window: typically three Michel tracks/event) (bartender, 400 ns window: typically three Michel tracks/event)  Computation times & performances  Future improvements & To Do’s  Comments and conclusions  Introduction to an alternative algorithm (Lecce group)

3. Algorithm strategy 1) 23/10/2013 Fabrizio Cei 3 Look at “triplets” of hits on the basis of wire number (Franco’s suggestion): Look at “triplets” of hits on the basis of wire number (Franco’s suggestion): One hit on plane i && One hit on plane i+1 && One hit on plane i+2 One hit on plane i && One hit on plane i+1 && One hit on plane i+2 Planes i and i+2 belong to the same view (u or v), plane i+1 to the other view. Planes i and i+2 belong to the same view (u or v), plane i+1 to the other view. i, u wire[i] To be included i, u wire[i] To be included i+1, v wire[i+1] “a priori” i+1, v wire[i+1] “a priori” i+2, u wire[i+2] i+2, u wire[i+2] Select hit combinations reasonably compatible with a positron track: Black: u view Black: u view Red: v view Red: v view Up to  16 wires crossed in other view Up to  16 wires crossed in other view Compute minimum path between hit wires  estimate of coordinates; Iterate procedure to form portions of tracks (“segments”); In planes belonging to the same view, track crosses “almost parallel” wires  wire[i+2]  wire[i] (  (3 ÷ 4))

4. Algorithm strategy 2) 23/10/2013 Fabrizio Cei 4 Merge segments with several hits in common; Skip segments fully contained in larger ones; Check the quality of the segments with circular fits; Remove spurious hits by contiguity criteria; Apply selections based on resolution to clean the segments; Perform merging of segments with similar estimated coordinates; Check if surviving segments are portions of the same track; Try to recover not yet assigned hits; Compare reconstructed segments with original ones by  2 for quality check. Evaluate performances and computation times as function of adopted selections.

5. Merging and cleaning 23/10/2013 Fabrizio Cei 5 Merging strategies 1) 2) 3) All hits in common A segment fully contained Very similar reconstructed except one  wire-merged in an other  skipped coordinates   2 -merged Cleaning strategies 1) 2) 1) 2) Black: reconstructed hits Green: true hits smeared with resolution Contiguity: red hit too far from Resolution: red hit too far from true hits previously reconstructed hits

6. Intrinsic inefficiencies 23/10/2013 Fabrizio Cei 6 All wires in the same plane Missing wires (one view only at the acceptance borders)

7. Parameters 23/10/2013 Fabrizio Cei 7 Maximum difference in wire number between planes: i and i+1:  n i,i+1 Maximum difference in wire number between planes: i and i+2:  n i,i+2 Contiguity cuts:  Z c,  X c,  Y c Resolution cuts:  Z r,  X r,  Y r  2 cut to define a good merging between segments Same  2 used to define a “well reconstructed segment” (wrt the true one) Tension between (efficiency, reconstruction quality) Tension between (efficiency, reconstruction quality) (= choose the highest possible numbers) and (= choose the highest possible numbers) and (combinatorial background, computation time and needed memory) (combinatorial background, computation time and needed memory) (= choose the lowest possible). (= choose the lowest possible). Representative values (rather conservative, not optimized):  n i,i+1 = 16,  n i,i+2 = 4,  Z c =20 cm,  X c,  Y c = 5 cm,  Z r =20 cm,  X r,  Y r = 5 cm,  2 = 15

8. Pure signal track: xy 23/10/2013 Fabrizio Cei 8 True segments: 4 Formed segments: 334 Wire-merged: 209 Skipped: 96 Surviving: 29  2 -merged: 21 Continuity with previous tracks: 4 Surviving at the end: 4 Fraction of assigned hits: 94.7%

9. Same event: yz & xz 23/10/2013 Fabrizio Cei 9 Larger uncertainty in Z coordinate, as expected.

10. Same event mixed with 4 Michel positrons: xy 23/10/2013 Fabrizio Cei 10 True segments: 9 Formed segments: 1131 Wire-merged: 528 Skipped: 496 Surviving: 107  2 -merged: 78 Continuity with previous tracks: 17 Surviving at the end: 12 Fraction of assigned hits: 87.6%

11. Same event mixed with 4 Michel positrons: yz & xz 23/10/2013 Fabrizio Cei 11 Larger uncertainty in Z coordinate, as expected.

12. 200 superimposed signal tracks: yx 23/10/2013 Fabrizio Cei 12  Black: original hits  Different colours: reconstructed tracks reconstructed tracks  No events outside the acceptance acceptance  Inefficiency at the borders of acceptance, borders of acceptance, where only one view is where only one view is equipped with sensitive equipped with sensitive wires. wires. N.B. Typically no TC hit N.B. Typically no TC hit for these tracks. for these tracks.

13. 200 superimposed signal tracks: yz & xz 23/10/2013 Fabrizio Cei 13 Acceptance fully covered; no regions with black dots only.

14. 200 superimposed signal tracks:  X,  Y e  Z vs true values 23/10/2013 Fabrizio Cei 14  X  = 1.8 mm  Y  = 2.2 mm  Z  = 1.3 cm

15.  2 for signal tracks 23/10/2013 Fabrizio Cei 15 Note the log-scale ! log-scale ! Well reconstructed segments  2 cut

16. Fraction of well reconstructed segments: 200 signal tracks 23/10/2013 Fabrizio Cei 16 > 0.5: 97 % > 0.75: 87 % > 0.8: 80 % 1: 71.5 % Always at least one good segment per track Computation time: 0.25 s/event 0.25 s/event A lot of input-output for checking purposes  probably overestimated True segments: 774 Reconstructed: 6770  770 at the end

17. 200 superimposed signal tracks: fraction of assigned hits 23/10/2013 Fabrizio Cei 17 92.5 %

18. Perfomances vs parameters for pure signal tracks 23/10/2013 Fabrizio Cei 18 N/A = not applied

19. Adding the background... 23/10/2013 Fabrizio Cei 19

20. 200 signal tracks + Michel positron background: yx 23/10/2013 Fabrizio Cei 20  Black: original hits  Different colours: reconstructed tracks reconstructed tracks  Again, no events outside the acceptance the acceptance  Most of these tracks are outside the TC coverage outside the TC coverage

21. 200 signal tracks: signal + Michel positron background: yz & xz 23/10/2013 Fabrizio Cei 21 Outside the acceptance

22. 200 superimposed signal + Michel tracks:  X,  Y e  Z vs true values 23/10/2013 Fabrizio Cei 22  X  = 2.3 mm  Y  = 2.6 mm  Z  = 1.1 cm

23. Fraction of well reconstructed segments: signal + Michel tracks 23/10/2013 Fabrizio Cei 23 > 0.5: 86.5 % > 0.75: 57 % > 0.8: 45.5 % 1: 19 % At least one well reconstructed segment in any track Computation time: 0.3 s/event 0.3 s/event Including the background, the quality of the reconstruction worsens, but the algorithm still works: no tracks are completely lost. Representative case

24.  2 for mixed tracks 23/10/2013 Fabrizio Cei 24 Well reconstructed segments Note the log-scale ! log-scale ! Longer tail

25. Perfomances vs parameters for signal + Michel tracks 23/10/2013 Fabrizio Cei 25 Very difficult to handle Huge number of reconstructed segments  memory problems, very large computation time

26. Improvements and To Do’s 23/10/2013 Fabrizio Cei 26 Improve contiguity selection technique: distance from last hit  distance from track extrapolation; distance from last hit  distance from track extrapolation; More realistic evaluation of computation times by reducing the I/O operations; Refine the choice of cuts; Improve algorithm to associate separated segments of the same track (developed in Tiziano Rovai’s thesis); Convert the code from a C-MACRO to a meganalyzer task; Check performances and computation times in different background conditions:...

27. Comments & Conclusions 23/10/2013 Fabrizio Cei 27  A pattern recognition algorithm based on search for triplets is under development;  Algorithm uses selections based on contiguity and on an approximate knowledge of Z coordinate to clean segments and on similarity between segments of tracks of Z coordinate to clean segments and on similarity between segments of tracks to reduce their number; to reduce their number;  Algorithm behaves well for pure signal tracks, with good efficiency and recognition capabilities and with reasonable computing times; recognition capabilities and with reasonable computing times;  For mixed tracks, performances become worse as expected, but still reasonable and the computation times do not increase too much; and the computation times do not increase too much;  The approximate knowledge of Z-coordinate is crucial to avoid a too large number of reconstructed segments of tracks, while the contiguity based selection number of reconstructed segments of tracks, while the contiguity based selection is very effective in cleaning the segments from spurious hits. is very effective in cleaning the segments from spurious hits.

28. An alternative strategy for pattern recognition Department of Mathematics & Physics MEG Group of Lecce Meeting 23 October 2013 University of Salento – Lecce 23/10/201328 Fabrizio Cei

29. Goal: define a pattern recognition strategy based only on the hit wire number An alternative strategy for pattern recognition Recognize the turning point X – Z view The Drift Chamber geometry Fast reconstruction of the z–coord. based on crossed wires in the xz plane Vertex extrapolation 23/10/201329 Lecce group, shown by Fabrizio Cei

30. Tails coming out from hits far away from the Z = 0 plane An alternative strategy for pattern recognition Preliminary study on 1000 signal positron tracks from muon decay Gaussian fit results Mean = 0.0066 cm Sigma = 2.51 cm 23/10/201330 Lecce group, shown by Fabrizio Cei

31. Scatter plot of the z-coord. vs the distance from the longitudinal axis (radius) Radius at Z = 0 An alternative strategy for pattern recognition Preliminary study on 1000 signal positron tracks from muon decay 23/10/201331 Lecce group, shown by Fabrizio Cei

32. An alternative strategy for pattern recognition Testing this procedure on a sample of signal event + pile-up, without taking into account the trigger. All combinations between track segments are considered Suppressing the spurious combination and tuning the selection criteria is possible to improve the resolution 23/10/201332Lecce group, shown by Fabrizio Cei

33. Next steps Define the selection criteria to suppress the spurious sequences Kinematical parameters evaluation Select the best hit sequence for the tracking step An alternative strategy for pattern recognition Study of the performances with increasing pile-up ev. 23/10/201333 Lecce group, shown by Fabrizio Cei

34. Backup slides 23/10/2013 Fabrizio Cei 34

35. 200 superimposed signal tracks 23/10/2013 Fabrizio Cei 35