1. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 1 Software Alignment of the CMS Tracker V. Karimäki / HIP V. Karimäki / HIP Workshop on B/Tau Physics at the LHC Helsinki, May 30 - June 1, 2002 Topics:  General considerations  Strategies  Algorithms  Helsinki auto-alignment algorithm  Concluding remarks

2. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 2 General considerations

3. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 3 Alignment processes - hardware + software Precision assembly Initial positions (modules) Monitoring information Positions corrected by monitoring Alignment by tracks Surveys in situ For once ‘Final’ calibrated positions Once a year …? ‘Continuous ’ ? For every shot? Signal

4. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 4 Detector alignment by tracks - why, how Why  Precision after assembly and optical surveys 0.1 - 0.2 mm (?)  Needs about 0.5 * hit resolution i.e. 5 - 30  m  Magnetic field effects, temperature effects How  Utilising natural smoothness of particle trajectories  Using high p T tracks  Misalignments systematic offsets of hits from trajectories  Software algorithm(s) to reduce systematic offsets by correcting the detector positions

5. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 5 Elementary alignment ‘manually’ 1D EXAMPLE

6. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 6 Importance of alignment precision Example: Error in local u-coord due to tilt   u ~ u tan     u = 10  m  = 45 o  = 45 o u = 5 cm u = 5 cm Implies:  = 0.2 mrad = required angular precision  u Tilt angle 

7. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 7 Algorithm development Formulations, basic tools:  Dependence of correction parameters on residuals - can be complicated   2 minimization, Kalman Filter techniques, linear algebra - standard techniques  misalignment tools (for development and validation)  track reconstruction Algorithms validation:  Monte Carlo simulation - comparison of known misalignments with corrections obtained by the algorithm - pull values  Test-beam data - improvement of hit resolutions, trajectory quality  Alignment contest! ; referee to prepare recHit data set with misaligned detector ; the algorithms should find the misalignments within errors

8. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 8 CMS misalignment tool Helge Voss Britta Schwering Tapio Lampen

9. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 9 Misalignment tool use cases  Study of misalignment effects on reconstruction  Development and testing of alignment algorithms Movement rods/wedges  x =  y =  z =1000  m: Z  events Helge Voss:

10. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 10 Discussion of strategies

11. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 11 Hierarchy and application strategy Hierarchy of alignment corrections: -full detector -barrel, F/B detectors -barrel, F/B detectors -barrel layers, forward disks -barrel layers, forward disks -barrel rods, forward wedges -barrel rods, forward wedges -detector modules (assumed planar) -detector modules (assumed planar) i.e. factorization of the problem when working on the alignment Alignment correction mappings: -rotation, translation, 3+3=6 parameters per unit -sag, twist, 2 or 3 parameters typically per unit (not for modules) Application strategy: Compute and transform all global corrections down to the lowest level, i.e. to the detector modules Aligned reconstruction geometry = ideal geometry + wafers position/orientation corrections position/orientation corrections

12. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 12 Software alignment strategies Distinguish: 1) Alignment start-up (launched at Day 1)  input is ‘best geometry’ by assembly, survey and monitoring  ‘large’ corrections  steep (human) learning curve  tedious, time taking 2) Alignment calibrations (at regular intervals)  input is previous best alignment + monitoring information  repetition rate 1 day or more (experience only tells)  ‘small’ corrections  learning curve levelling off  might become routine-like  yet always room for improvements (algorithms, statistics, …)

13. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 13 Possible schedule for alignment start-up Preparations:  Work out estimates of alignment errors (important for pattern recognition)  Further tuning of track reconstruction  Using isolated particles (high p_T muons) Work inside out:  Semi-independent alignment of Pixel detector ; tracks curvature by full tracker, especially for 2-layer Pixel ; vertex constraint important (therefore start with Pixel) ; hits only for Pixel independent alignment ; determines the coordinate system ; given elements need to be fixed (simulations will help to tell us)  Continue with TIB, TOB, …  Matching between Tracker parts  Matching with muon chambers Iteration cycles

14. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 14 Sagitta and spurious sagitta Sagitta: largest distance cord to arc Spurious sagitta: change due to systematic errors in hit position = a measure of misalignments

15. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 15 Curvature accuracy for Pixel alignment SPURIOUS SAGITTA In Pixel In Tracker sagitta is proportional to L 2 consider 2-layer Pixel sagitta error (Pixel) / sagitta error (Tracker) ~ (7.2/105) 2 ~ 0.005 We conclude: 1 mm sagitta error due to misaligments in full Tracker reflects only 5  m sagitta error in 2-layer Pixel We get precise enough curvature determination from misaligned Tracker for (semi)independent Pixel alignment Can we align Pixel independently of the rest of the Tracker on Day 1? Yes, if we can obtain precise enough curvature using full Tracker:

16. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 16 Candidate algorithms

17. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 17 Candidates for alignment algorithms - 1  Alignment by Kalman Filter method ; Fruhwirth et al., CMS Note-2002/008 ; uses annealing to avoid secondary minima ; 3-parameter alignment tested with simulated test- beam like setup  Helsinki auto-alignment method   2 minimization formalism ; iterative, several passes over given data ; up to 6 parameters per module ; successfully applied to real test-beam data (silicon telescope) with 5 parameter alignment ; mathematics of the algorithm are simple ; involves small matrices ; ORCA implementation under work

18. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 18 Candidates of alignment algorithms - 2  H1 method (Gabathuler/PSI) ; used for H1 vertex detector ; algorithm (implicit vertex constraint): k all pairs of tracks k minimizing sum of squared distances in space between all track pairs k mathematics of the algorithm complicated  Blobel method (Raupach/Aachen)   2 solution of a very large number of parameters ; CMS/Aachen people...  A large number of algorithms exist, more than one per experiment, experiment specific

19. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 19 Brief description of Helsinki algorithm

20. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 20 Helsinki auto-alignment - 1

21. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 21 Helsinki auto-alignment - 2

22. Workshop on B/Tau Physics, Helsinki 30.5.-1.6.2002 V. Karim ä ki, HIP 22 Concluding remarks Aiming at: Toolkit for tracker alignment with tracks = auto-alignment toolkit Providing an effective (default) algorithm Stand-alone version for simulation of telescope-like setup Tracker auto-alignment simulation in ORCA framework Status: Mathematical formulation of an effective algorithm: derived, tested Used successfully in test-beam environment (CMS NOTE 2000/013) OO modeling and coding of the 'core' classes: first iteration Simplified telescope-like alignment simulation: first results Interface with ORCA: started Future work: Development of ORCA interface Studies of auto-alignment for chosen parts of the Tracker Studies of using constraints (beam, vertex, $Z^0$-kinematics,\dots) Studies of correlated modules alignment etc...