1. ITS Alignment: Millepede Results S. Moretto, C. Bombonati, A. Dainese, M. Lunardon, A. Rossi

2. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008Contents: Alignment Strategy and Task Millepede Method: – –Idea of Millepede – –the ITS Millepede Class Validation of the strategy with simulation: – –tests and results with Millepede First Cosmic Data: – –Results and Status of the alignment with Millepede

3. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 ITS Alignment Task Tracking detectors in high-energy physics experiments require an accurate determination of a large number of alignment parameters in order to allow a precise reconstruction of tracks and vertices. In addition to the initial optical survey, the use of tracks in a special software alignment is essential. As an example, for the pixel detectors, whose position resolution is about 12  m in the most precise direction, a residual misalignment not larger than 10  m can be tolerated. The task of aligning the ALICE ITS is particularly challenging also due to the very large number of degrees of freedom, which are about 13,000. The ITS alignment procedure will use tracks from cosmic-ray muons (data taking started in February 2008), and tracks from pp collisions that will be collected next year.

4. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 ITS Alignment Stategy For the alignment of the ALICE Inner Tracking System two independent methods, based on tracks-to-measured-points residuals minimization, are being prepared. One method performs a (local) minimization for each single module and accounts for module correlations by iterating the procedure until convergence is reached. The second method uses the Millepede approach, where a global fit to all residuals is performed, extracting all the misalignment parameters simultaneously.

5. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede Starting Point The original development of the Millepede method has been done by V. Blobel (http : www.desy.de/blobel/wwwmille).www.desy.de/blobel/wwwmille All LHC experiments make use of Millepede method. In ALICE framework, in particular, AliRoot, it was first implemented by the MUON spectrometer group (J. Castillo et al.) and now, a dedicated alignment class has been created (AliITSAlignMille) for ITS.

6. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede Idea In an alignment environment, the track data are position measurements of a charged particle track. The position measurement, from several detector planes of the track detector, depend on the position and orientation of certain sensors, and the corresponding coordinates and angles are global parameters A practical limit for the number of global (alignment) parameters is about ten thousands Millepede is a method to solve the linear least squares problem with a simultaneous fit of all global (alignment) and local (track) parameters, irrespectively of the number of local parameters.

7. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede Strategy Main requirement of Millepede approach is that the measured value, the residual, i.e. the deviation between the measured and the fitted data, can be well approximated with a linear function of the track (= local, q k ) and alignment (= global, p l ) parameters. For a set of N local measurements one obtains a system of least squares normal equations with large dimensions

8. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede for the ITS We can summarize the ITS alignment algorithm in the following steps: 1. 1. Initialization from a configuration file (list of modules to be aligned, constraints, starting geometry); 2. 2. Calculation for each track of the local and global derivatives at each hit and filling the corresponding local equations; 3. 3. Local (track) fits; 4. 4. Global (alignment parameters) fit.

9. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede Results with MC data Promising results have been obtained with a sample of 50000 simulated cosmic muons crossing both SPD layers. A realistic misalignment is applied to the sensors : for example, SPD: significant misalignments for BARREL (-300  m, -300  m, 500  m, -30mdeg, 40mdeg, -150mdeg), (-300  m, -300  m, 500  m, -30mdeg, 40mdeg, -150mdeg), HB, Sectors, Half-Staves and Ladders HB, Sectors, Half-Staves and Ladders The considered modules to be aligned are about 1/3 of the whole ITS and we considered 12 points tracks (two points for each single ITS layer). 655 modules ( 142 + 108 + 405 ) = ( 59% SPD + 41% SDD + 24% SSD )

10. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 X loc Y loc Z loc MC Results: single module alignment SPD SDD SSD

11. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Summary results for MC cosmic data All mean values for SPD and SDD ~ 0  m RMS around 10 micron (*)values in  m or mdeg PARAM SPD SDD SSD meanrms meanrms meanrms X 06 09 016 Y 210 17 -6060 Z 06 011 565 Psi 119 -216 -8164 Theta -210 16 018 Phi 171 124 -14120

12. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 ITS tracking resolutions: d 0 r  ITS tracking stand-alone no misalignment full mis + perfect realign full mis + Millepede realign (all ITS) full mis + Millepede realign (only realigned modules ~500: |  /2|<.5 && |  -  /2|<.5)

13. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede with cosmic data Statistics up Sep. 3rd 2008 58400 total tracks 30300 with 4 pts in SPD (used for Millepede) 24200 with 3 pts in SPD

14. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede Strategy: Hierarchical Alignment step 1HALF BARREL SPD step 2SECTORS SPD step 3HALF STAVES SPD step 4 LADDERS SPD step 5 step 5SPD position optimized wrt SSD step 6LADDERS SSD & SPD FIXED step 7HALF LADDERS SSD & SPD FIXED SPD SSD SDD: will be included once calibrated

15. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 SPD Alignment Status: SPD Alignment Status: Statistics up Sep. 3rd 2008 = 75% of full SPD (90% of alignable modules)StavesHalfStavesLaddersStat>053102202 Stat>505198180 Aligned modules Statistics:StavesHalfStavesLaddersStat>058111220 Stat>5055103200 Alignable modules:

16. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede Results: Residuals Track: 3-points fits on SPD and look at residuals on SSD

17. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Residuals: Raw and Millepede SSD INNER SSD OUTER SSD INNERSSD OUTER

18. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede Results: delta X One meaningful observable of the realignment quality is the mismatch in X of the tracks @ Y=0

19. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede Results for SPD Hierarchical Alignment Alignment of SPD in 4 steps: sectors -> staves -> half staves -> ladders

20. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 SPD alignment status: delta X final result Using the full sample of tracks to realign and to check the results MEAN= 0.9  m SIGMA= 55  m Compatible with a spatial resolution of ~ 15  m

21. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede: Extra Clusters TRACK-EXTRA CLUSTER DISTANCE IN THE TRANSVERSE PLANE Realignment of data with overlapping clusters:  overlapping clusters not used in the alignment  gaussian peak (small tails) sigma ~ 20-22  m spatial resolution ~ 14-16  m

22. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 SSD Alignment Status To recall the alignment of SSD procedure: alignment of SSD with the SPD already aligned – –SPD position optimized wrt SSD (raw data) – –SPD fixed and Ladders SSD – –SPD fixed and Half Ladders SSD meanXsigmaXmeanZsigmaZ raw14787326 ladders-236-10262 HL36*-3214 Results for the Delta X (Z) @ Y=0 [abs(X 0 )<1 cm] (*) Fitting the peak in [-0.060, 0.060] => sigma = 28  m, to be compared with perfect simulation (17  m)

23. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Stability Test for Millepede results Stability test with 10k-tracks samples DeltaX @ Y=0 plots with same alignment file From TrackMeanSigma 0-1054.2 10000-253.1 200000.952.5 300002.154.3 400002.153.6 500001.351.7 Very small differences along the whole cosmic data sample

24. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede Code: Status The development and debugging of the code is almost completed The development and debugging of the code is almost completed Possible improvements might be obtained with further analysis of the data Possible improvements might be obtained with further analysis of the data Hierarchical realignment (ITS Layers, HB, sectors,..) already validated Hierarchical realignment (ITS Layers, HB, sectors,..) already validated The Millepede code for B>0 (helix tracks) has been already implemented. The Millepede code for B>0 (helix tracks) has been already implemented. The code has been verified with simulation data: similar results wrt B=0 case with NULL misalignment.

25. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008Conclusions Millepede with MonteCarlo simulation has been crucial:   to optimize the code   to understand the strategy   to validate the results Millepede RESULTS with first cosmics data:   hierarchical realignment ready and validated useful to get information with medium-low statistics   Overall performance of alignment quite stable   SPD Alignment: from width of track-to-track distance plot and overlapping cluster distance, a spatial resolution of about 14-16 micron is extracted;   SSD Alignment: alignment performed at the level of Half-Ladder   SDD Alignment: ready to be included as soon as the calibration has been done

26. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 more and more

27. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Residuals: Raw and Millepede SPD INNER SPD OUTER SPD INNER SPD OUTER

28. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Millepede: aligned modules Configuration with 500 modules Configuration with 500 modules |  /2|<.5 && |  /2|<.5) |  /2|<.5 && |  /2|<.5)  vs  of realigned modules: “aligned solid angle”

29. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 M. Lunardon - ITS Alignment Meeting – CERN – 5.08.2008 Alignment with even tracks (15k used) Check with odd tracks All odd tracks:sigma = 55 mu area 3 sigma = 89% SPD alignment status Stability test with even/odd tracks

30. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 Realignment of data with overlapping clusters orthogonal distance number of pairs meandistance all tracks 25500.2 22.5 +- 0.4 abs(x0)<1cm8500.1 21.4 +- 0.6 SPD1 && abs(x0)<1cm 440 22.2 +- 0.9 SPD0 && abs(x0)<1cm 4101.1 19.6 +- 0.8 - overlapping clusters not used in the alignment - gaussian peak (small tails) - sigma ~ 20-22 micron => spatial resolution ~ 14-16 micron SPD alignment status

31. S. Moretto Convegno Fisica di Alice Palau, Settembre 2008 The matrix on the left side of equation (12) has, from each local measurement, three types of contributions. The first part is a contribution of a symmetric matrix C1j, of dimension n (number of global parameters), and is calculated from the (global) derivatives. The second contribution is the symmetric matrix  j, which gives a contribution to the big matrix on the diagonal and is depending only on the j-th local measurement and the (local) derivatives. The third (mixed) contribution is a rectangular matrix Gj, with a row number of n (global) and a column number of (local). There are two contributions to the vector of the normal equations (gradient), g1j for the global and j for the local parameters.