1. 1 naustin@mail.cern.ch1 Endcap C SCT Efficiency Calculation Update Nicholas Austin University of Liverpool Operations Meeting June 2007

2. 2 Want to calculate the efficiency of the SCT modules in the endcap C. Need to optimise the road width to be used in this calculation. Original plan to extrapolate TRT tracks into SCT and compare positions with hit RDO strips SCT Endcap C Module Efficiency Calculation… Original Plans

3. 3 Discovered that internal back tracking tool was not suited for this task Bad resolution of TRT measurements give great errors when fitting the track. Only tracks with many SCT space points are reconstructed well, however, In order to remove biases from efficiency calculation, SP’s in active disk have to be removed and tracks refitted. This causes more problems with bad reconstruction and low statistics. Basically the backtracking is a black box which we do not understand. It has been decided to abandon this method in favour of one that does not use tracks or backtracking at all. SCT Endcap C Module Efficiency Calculation… Problems with Original Plans

4. 4 No track cuts!!! (we don’t understand backtracking so don’t want to use it. Require 2 or more space points Loop over disks/sides Loop over SP’s Find and count all SP’s NOT in active disk, and Store their global positions and corresponding disk numbers Require 2 or more space points not in active disk Loop over all modules in the active disk Loop over pairs of SP’s not in active disk Take one SP as starting position, obtain direction from their relative positions, extrapolate to every module in the active disk. If extrapolation is fiducial  predictedhit = true Loop over RDO’s Find RDO strip hits in active module. If RDO strip passes through predicted area of predicted hit, efficient = true for active module efficient = false predictedhit = false disks SP’s New Method – Extrapolate SCT Space Point Pairs

5. 5 Loop over disks/sides Loop over SP’s Find and count all SP’s NOT in active disk, and Store their global positions and corresponding disk numbers Require 2 or more space points not in active disk Loop over all modules in the active disk Loop over pairs of SP’s not in active disk Take one SP as starting position, obtain direction from their relative positions, extrapolate to every module in the active disk. If extrapolation is fiducial  predictedhit = true Loop over RDO’s Find RDO strip hits in active module. If RDO strip passes through predicted area of predicted hit, efficient = true for active module active disk efficient = false predictedhit = false New Method – Extrapolate Space Point Pairs, continued.

6. 6 Loop over disks/sides Loop over SP’s Find and count all SP’s NOT in active disk, and Store their global positions and corresponding disk numbers Require 2 or more space points not in active disk Loop over all modules in the active disk Loop over pairs of SP’s not in active disk Take one SP as starting position, obtain direction from their relative positions, extrapolate to every module in the active disk. If extrapolation is fiducial  predictedhit = true Loop over RDO’s Find RDO strip hits in active module. If RDO strip passes through predicted area of predicted hit, efficient = true for active module efficient = false predictedhit = false New Method – Extrapolate Space Point Pairs, continued.

7. 7 Loop over disks/sides Loop over SP’s Find and count all SP’s NOT in active disk, and Store their global positions and corresponding disk numbers Require 2 or more space points not in active disk Loop over all modules in the active disk Loop over pairs of SP’s not in active disk Take one SP as starting position, obtain direction from their relative positions, extrapolate to every module in the active disk. If extrapolation is fiducial  predictedhit = true Loop over RDO’s efficient = false predictedhit = false Find RDO strip hits in active module. If RDO strip passes through predicted area of predicted hit, efficient = true for active module New Method – Extrapolate Space Point Pairs, continued.

8. 8 SCT Efficiency Road Width Calculation – Method Summary and Geometry correction Extrapolate straight lines through space point pairs into the ‘active disk’. Compare intersect positions of the extrapolated lines and the SCT modules, with ‘RDO hits’. Plot distance/residual between the extrapolated positions and the ‘hit strips’ ‘dist’ is the correct distance that we need to measure. Extrapolated ‘Predicted Position at (x extrap,y extrap )‏ RDO hit = centre of a strip that has detected the cosmic particle, (x rdo,0) Using similar triangles: W = (Wmax + Wmin) / 2 r = W*L / (Wmax – Wmin)‏ dist = X rdo * (1 + Y extrap /r) - X extrap

9. 9 Efficiency Method (A) to calculate efficiency for each disk and side  ij = N(predicted hits with rdo strip hits near by, in disk i, side j) N(predicted hits in disk i, side j) = N(predictedhit + efficient) N(predictedhit) For each layer (disk, side)… Count the number of times there is a predicted hit (denominator). Count the number of times there is a predicted hit with a strip hit near (numerator).

10. 10 Method usually works quite well...

11. 11... But some don’t work… Predicted hits where there blatantly shouldn’t be predicted hits!

12. 12 Problems arise when there are extrapolations to multiple modules in the same disk. This is usually as a result of having >1 SP in a disk. Possible fixes:  Only except extrapolations in a particular angle range.  Only except extrapolations that pass through both trigger counters. New Efficiency Method:  Look at the ratio of single to double hits. This would give efficiencies for each disk without using extrapolations that have no nearby strip hit.

13. 13 Define efficiency of hit on one side of particular disk =  Then, for each disk… Count Ratio: R = N(double sided hits) / N(single + double hits) = 0 000 or P( ) =  (1-  ) + (1-  )  +  2 =  (2-  ) =  2  R =  /(2-  ), and calculate the disk efficiency   = 2R/(1+R) 1 111 Error in ,d  = (de/dR) dR = {-2R/(1+R)2 + 2/(1+R)} dR (where dR = binomial error of Ratio)‏ X X X X X X X X ) New Ratio Method (B) to calculate efficiency for each disk

14. 14 Only gives 'side efficiencies' for each disk (  i = efficiency of one side of disk i). but automatically only uses ‘good’ extrapolations to modules where there should be hits. New Ratio Method (B) to calculate efficiency for each disk… Advantages

15. 15 Also (simple fix), to really clean up the dataset and remove many fake extrapolations, remove all events where there is more than one space point on any particular disk.

16. 16 Results from Last Time... Previously did not understand the weird bumps in the distribution. These bumps appear on the left of the peak for side 0, and the right for side 1. Turned out to be times when I was comparing strip hits on the correct side of the module with extrapolated positions on the wrong side of the module. Stereo angle between sides explains the periodic nature, and the ~2mm shift of the bumps. This has been fixed, also a couple of double counting issues!!!

17. 17 Results after fix... Residuals for Disk 1  inner >  outer WHY???

18. 18 Sigma of Residuals Plots Why is disk 2 so large? Why are the sides so different? Especially the Errors?

19. 19 Efficiencies, Method A

20. 20 Efficiencies, Method B

21. 21 Looping over SP pairs means multiple extrapolations to each layer per event. This gives a strange predicted area. Not the best definition for efficiency. Want to use all space points outside the active layer to fit one single straight line that is to be extrapolated to the active layer and compared to RDO hits. Perform a minimisation of the sum of the squares of the residuals (distances between the space point positions and the fitted track). Introducing a Least Square Fit Extrapolation Method

22. 22 Require 2 or more space points and no more than one space point in any one disk Loop over disks Loop over SP’s Find and count all SP’s NOT in active disk, and Store their global positions and corresponding disk numbers Require 2 or more space points not in active disk… Perform least squares fit on SP’s not in active disk  x0[3] (arbitrary starting point on fitted line)  dir[3] (direction of fitted line). Loop over sides Loop over all modules in the active layer Extrapolate least square SP fit to active module. If extrapolation is fiducial (will only happen once per disk/side)  predictedhit = true Loop over RDO’s Find RDO strip hits in active module. If RDO strip passes through predicted area of predicted hit… bool efficient = false bool predictedhit = false What the code looks like now – Two efficiency methods and a Least Squares Fit bool hitonside0 = false bool hitonside1 = false efficient = true for active module. if(side==0) hitonside0 = true; if(side==1) hitonside1= true; if(predictedhit) Fill m_EfficiencyHistTot for disk, side. if(efficient) Fill m_EfficiencyHistEff for disk, side. if(hitonside0 || hitonside1) Fill m_singlehitcount for disk. if(hitonside0 && hitonside1) Fill m_doublehitcount for disk. disks SP’s x

23. 23 Want to minimise the squares of the differences between data points and the fit in two projections: Minimise S =  i (z i - (p 1 x i + p 2 )) 2 +  i  (z i – (q 1 y i +q 2 )) 2 p 1 = n  i x i z i –  i x i  i z i n  i x i 2 - (  i x i ) 2 q 1 = n  i y i z i –  i y i  i z i n  i y i 2 - (  i y i ) 2 q 2 = 1/n (  i z i - q 1  i y i ) p 2 = 1/n (  i z i - p 1  i x i ) Choose 2 arbitrary z points and calculate x and y. Use one of the points as a ‘starting position’ and the relative position of one w.r.t. the other as a ‘direction’ for the extrapolation. z = p 1 x + p 2 ==> x = (z - p 2 )/p 1 z = q 1 y + q 2 ==> y = (z - q 2 )/q 1 The Least Squares Fit of Space Points not in the Active Layer… How is it done? ==>

24. 24 Residuals from Least Square Fit Method Cuts: 2+ SP's in event and no more than one SP in any disk.  inner >  outer WHY???

25. 25 Mean of Residuals from Least Square Fit Method Cuts: 2+ SP's in event and no more than one SP in any disk.

26. 26 Sigma of Residuals from Least Square Fit Method Cuts: 2+ SP's in event and no more than one SP in any disk. Again... why are the two sides so different??? Especially the errors? Need to look into this!!!

27. 27 Efficiencies (Method A) from Least Square Fit Method Cuts: 2+ SP's in event and no more than one SP in any disk.

28. 28 Efficiencies (Method B) from Least Square Fit Method Cuts: 2+ SP's in event and no more than one SP in any disk.

29. 29 Comparison between two extrapolation methods (same cuts), Efficiency Method A. Disk, SideSP Pair Method Efficiency Least Square Fit Method Efficiency 0,00.842340.84859 0,10.842440.84717 1,00.849340.84393 1,10.844560.83911 2,00.887000.87778 2,10.882460.87129 3,00.856190.85884 3,10.849800.85317 4,00.808470.82728 4,10.803420.82505 5,00.526880.62092 5,10.525180.62939 6,00.00000 6,10.00000 7,00.00000 7,10.00000

30. 30 Comparison between two extrapolation methods (same cuts), Efficiency Method B. DiskSP Pair Method Efficiency Least Square Fit Method Efficiency 00.89180.8927 10.89380.8911 20.92420.9249 30.93630.9367 40.94110.9305 50.92830.9336 60.0000 7

31. 31 Comparison between two extrapolation methods (same cuts). Not much between the efficiencies derived from both extrapolation methods. The least square fit extrapolation does seem to improve the efficiencies ever so slightly. The least square fit extrapolation gives a much more definitive definition of efficiency (only one extrapolation per ‘experiment’. The least square fit extrapolation removes a loop from the code and makes it much simpler. Decided to discard the space point pair method in favour of the least square fit extrapolation.

32. 32 Summary so far… The code is now very straight forward and both efficiency methods are well defined due to the single extrapolation achieved with a least squares fit. However, the efficiencies still seem to be rather low. The code no longer uses track information, only Space Points. As we cannot cut on the number of space points without biasing the results I am limited in how much I can clean up the sample. I need to look at other explanations as to why my efficiencies are low. Method A Method B

33. 33 Discussion with Helen, Sergey and Andy… Do we have low energy muons scattering off silicon surfaces? Look at the energy and transverse momentum of the truth muon Look at the incident angles of the truth muon and the extrapolated track at module surfaces. Where does the truth muon go when the SP extrapolation is not efficient? Compare the number of times a muon has single and double sided hits with that for the truth muon. Do we have nasty showers or scattering from the detector material. Should this be happening in Monte Carlo? Plot the number of space points and tracks per event. Also I need to understand why the residuals for the inner modules are so much wider than those for the outer and middle? Need to run over SR1 data. May be a good idea to also look at beam halo and gas Monte Carlo. This will require upgrade to v.13. Upgrading would be a good idea anyway! I am the only person in ATLAS using v.12.0.3-COS!!!

34. 34 Latest Progress… I have added the truth information A starting position (vertex) and a direction (momentum) for the truth muon can be obtained from the McEventCollection. The truth muon can then be extrapolated in the same way as the least square space point fit to each disk. Residuals and efficiencies for both methods have been calculated using the extrapolation of the truth muon. Properties of the truth muon have been compared with those of the extrapolated track, including direction and incident angles at surfaces.

35. 35 Residuals: SP Extrap vs RDO Hits and Truth Muon Extrap vs RDO Hits Disk 0, Side 0 Disk 0, Side 1 Disk 1, Side 0 Disk 1, Side 1 Outer Middle Inner All distance scales are in mm

36. 36 Residuals: SP Extrap vs RDO Hits and Truth Muon Extrap vs RDO Hits Outer Middle Inner Disk 2, Side 0 Disk 2, Side 1 Disk 3, Side 0 Disk 3, Side 1

37. 37 Residuals: SP Extrap vs RDO Hits and Truth Muon Extrap vs RDO Hits Outer Middle Disk 4, Side 0 Disk 4, Side 1

38. 38 Residuals: SP Extrap vs RDO Hits and Truth Muon Extrap vs RDO Hits Truth muon residuals are all nice gaussian peaks centred at zero and all have small widths. SP extrapolation residuals are not so good. Especially for inner disks. Notice sign of shift of SP Extrap residual is periodic with disk number.

39. 39 Sigma of Residuals… Truth Muon and S.P. Extrapolation

40. 40 Efficiencies for Method A… Truth Muon and S.P. Extrapolation

41. 41 Efficiencies for Method B… Truth Muon and S.P. Extrapolation

42. 42 Efficiencies for Methods A and B… Truth Muon and S.P. Extrapolation A B

43. 43 Event Statistics Each event in the MC sample only has one truth particle… a muon. However, each event has multiple tracks. These tracks must either come from noise (?) or low energy muon scattering.

44. 44 As expected, more muons with low energies than higher energies. But there has obviously been a cut at 80GeV. Are these energies low enough for scatter effects? Kinematics of the Truth Muon

45. 45 Comparisons between the directions of the truth muon and the S.P. extrap. N.B. There are more entries for the S.P. Extrapolation as each collection of space points undergoes multiple extrapolations to each disk.

46. 46 Comparisons between the directions of the truth muon and the S.P. extrap.

47. 47 Hit positions of Efficient and Inefficient S.P extrapolated hits. Seems to be a concentration of inefficient hits at the tops of modules. Need to look closer at “zcol” plots to really look at this.

48. 48 Hit positions of Truth muon extrapolated hits. Here the red dots correspond to times when the S.P. Extrapolation is inefficient, not the truth muon extrapolation!

49. 49 “Relative” Residuals of Efficient S.P. Extrapolations.

50. 50 “Relative” Residuals of Inefficient S.P. Extrapolations.

51. 51 Angular distribution of Efficient and Inefficient S.P extrapolated hits.

52. 52 Angular distribution of Truth muon extrapolated hits. Here the red dots correspond to times when the S.P. Extrapolation is inefficient, not the truth muon extrapolation!

53. 53 Angular Residuals of Efficient S.P. Extrapolations.

54. 54 Angular Residuals of Inefficient S.P. Extrapolations.

55. 55 Cutting on the number of Space Points. When I was extrapolating TRT tracks in order to calculate the efficiencies I was able to clean up the data set by cutting on the quality of the track. The current version of the code only uses SCT space points. The only thing to cut on is the number of SCT space points. It is obvious that cutting on this will bias the results (since extrapolations are compared to RDO hits… two of which form a space point). However, by accident I ran with a cut requiring an event to have 3 or more space points. Of course this has increased the efficiencies. Could this be counted as a good track cut?

56. 56 Sigma of Residuals… Truth Muon and S.P. Extrapolation (NSP>2 cut)

57. 57 Method A Efficiencies… Truth Muon and S.P. Extrapolation (NSP>2 cut)

58. 58 Method B Efficiencies… Truth Muon and S.P. Extrapolation (NSP>2 cut)

59. 59 Efficiencies (Method A and B)… Truth Muon and S.P. Extrapolation (NSP>2 cut)

60. 60 Still to do…

61. 61