1. Iterative local  2 alignment algorithm for the ATLAS Pixel detector Tobias Göttfert IMPRS young scientists workshop 17 th July 2006

2. 20th June 2006Tobias Göttfert, MPI für Physik2 The LHC ring  circular proton-proton collider at CERN  27 km circumference  will go into operation in 2007  has four experimental caverns for ATLAS, CMS, ALICE and LHC-b  provides a nominal center-of-mass-energy of 2·7 TeV with high luminosity  40 MHz collision rate, each collision produces ~1000 tracks

3. 20th June 2006Tobias Göttfert, MPI für Physik3 The ATLAS Experiment 44 m 22 m Inner Detector: TRT SCT Pixel 1,2m6,8 m TRT: Transition Radiation Tracker SCT: SemiConductor Tracker

4. 20th June 2006Tobias Göttfert, MPI für Physik4 The ATLAS Inner Detector SCT barrels: 4 layers Pixel (3 barrel layers; 3 endcap discs) TRT SCT endcap: 9 discs ~2.30m ~5.60m

5. 20th June 2006Tobias Göttfert, MPI für Physik5 Geometry of the Pixel detector  1744 modules: n + -on-n silicon detector 3 barrel layers, 6 endcap disks sensor area of 16,4 · 60,8 mm² 46080 pixels, each 50 · 400 µm² resolution:  x = 14,4 µm;  y = 115,5 µm x y z

6. 20th June 2006Tobias Göttfert, MPI für Physik6 Alignment - overview  Alignment = procedure to obtain best knowledge of all detector positions  Necessary for: Reconstruction of primary and secondary vertices (b-tagging) Good momentum resolution  study the mechanism of electroweak symmetry breaking, e.g. search for the Higgs boson  Measurement of W mass, top mass  b-physics, …  Required alignment precision (from ATLAS technical design report): PIXEL Local xLocal yLocal z required as-built + survey required as-built + survey required as-built + survey barrel1 - 7 µm50 µm20 µm 10 - 20 µm 50 µm endcap1 - 7 µm5 µm20 µm5 µm100 µm13 µm Alignment strategies: Survey after assembly Survey during running (e.g. laser interferometry in SCT) Track-based alignment

7. 20th June 2006Tobias Göttfert, MPI für Physik7 Track-based alignment residual # of hits reconstructed track real track  Use reconstructed tracks from many events  Use distribution of the residuals to determine alignment parameters  Residual = distance between the particle trajectory and the hit on the detector  For a detector at nominal position the distribution of residuals is centered around zero  For a shifted detector the distribution of residuals is shifted   minimize residual distributions

8. 20th June 2006Tobias Göttfert, MPI für Physik8 Local  2 -approach for track-based alignment Given the residuals r k, their errors  k and their derivatives dr k /da 0, we seek to minimize this  2 -function: by linearizing it, to get the alignment parameters a for each individual module (6 dimensional vector: 3 translations, 3 rotations)

9. 20th June 2006Tobias Göttfert, MPI für Physik9 Local  2 -approach for track-based alignment  Solution for the module’s parameters: all correlations between different modules were neglected  redoing track fits and iterating the procedure is necessary

10. 20th June 2006Tobias Göttfert, MPI für Physik10 Definition of residuals  One common definition of residuals for Pixel, SCT barrel and SCT endcap modules: Distance-of-closest- approach (DOCA) residuals SCT Pixel

11. 20th June 2006Tobias Göttfert, MPI für Physik11 Sample used for alignment studies  Alignment approach tested on a sample of 235000 simulated muons  originate from the nominal interaction point and illuminate the full Inner Detector  good tracks for alignment: no secondary interactions energy loss negligible momentum chosen to be greater than 10 GeV/c to minimize multiple scattering

12. 20th June 2006Tobias Göttfert, MPI für Physik12 Results Flow of the a x alignment parameter of all barrel modules during 10 iterations on nominal geometry

13. 20th June 2006Tobias Göttfert, MPI für Physik13 Results Flow of the alignment parameters of all barrel modules during 10 iterations on nominal geometry

14. 20th June 2006Tobias Göttfert, MPI für Physik14 Results Alignment parameter a x of all barrel modules after 10 iterations on nominal geometry

15. 20th June 2006Tobias Göttfert, MPI für Physik15 Results Alignment parameters of all barrel modules after 10 iterations on nominal geometry

16. 20th June 2006Tobias Göttfert, MPI für Physik16 Results Flow of the alignment parameter a x of 17 misaligned modules during 10 iterations initial misalignment blue: barrel modules red: endcap modules

17. 20th June 2006Tobias Göttfert, MPI für Physik17 Results Flow of the alignment parameters of 17 misaligned modules during 10 iterations initial misalignment

18. 20th June 2006Tobias Göttfert, MPI für Physik18 Results  Achieved alignment precision for this sample (235000 muon tracks): PIXEL barrelendcap σ gauss σ stat requiredσ gauss σ stat required a x [μm]9.919.721 - 71.650.715 1 – 7 a y [μm]62.155.32032.116.220 a z [μm]29.828.010 – 2013376.4100 a  [mrad]0.410.311.91.6 a  [mrad]0.810.705.45.1 a  [mrad]0.140.120.0610.043

19. 20th June 2006Tobias Göttfert, MPI für Physik19 CTB results  Approach was used on real data from the 2004 CombinedTestBeam (CTB)  6 Pixel modules and 8 SCT modules in the beam  Several pion runs with variable energies analysed and one common alignment derived with the algorithm

20. 20th June 2006Tobias Göttfert, MPI für Physik20 CTB residual distributions first iteration after 15 iterations Distribution of the x-residuals for one pixel module:

21. 20th June 2006Tobias Göttfert, MPI für Physik21 CTB alignment parameter flow

22. 20th June 2006Tobias Göttfert, MPI für Physik22 Summary  Starting point was the existing MPI approach for aligning the SCT detector  Software for Pixel detector alignment was developed and integrated into the common ATLAS software  Works by minimizing DOCA residual distributions for each module individually  Therefore needs iterating to handle correlation terms implicitly  Alignment precision of the approach was determined using a sample of simulated muons and real pion data  Final precision still needs more statistics additional constraints, e.g. vertex constraints  Lots of additional features already implemented or planned to improve the method