Alignment of the ATLAS Inner Detector Roland Härtel - MPI für Physik on behalf of the ATLAS inner detector alignment group Outline: LHC / ATLAS / Inner Detector Alignment approaches Results
Large Hadron Collider 27 km ring situated underground beneath Geneva High-energy protons (7 TeV) are circulated in the ring in two counter-rotating beams Start up end of this year! 7 TeV Protons ATLAS 7 TeV Protons ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 2
ATLAS Inner Detector ATLAS Extensive physics programme: Higgs, Top, Susy, Extra Dimensions, Inner Detector ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 3
Inner Detector Subdetectors Inner Detector has 1744 Pixel modules, 4088 SCT modules and 544 TRT modules (even more individual wafers and straw tubes) Pixel barrel SCT endcap TRT endcap ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 4
Inner Detector Alignment 3 different levels of alignment Level 1: subdetector, endcap, barrel (42 DoF) Level 2: layer, disk (444 DoF) Level 3: module (~ 35k DoF (Pixel + SCT) + O(1k) DoF (TRT)) Mounting and survey precision different for various subdetectors. About 100 μm Required alignment accuracy < 10 μm Must match or exceed intrinsic detector resolution (e.g. Pixel ~ 10 μm) to not degrade e.g. momentum resolution by more than 20% Requirement different for various subdetectors and DoF 6 DoF per alignable structure ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 5
Track-based alignment All track-based alignment relies on minimizing residuals Global χ 2 : minimization of χ 2 fit of all alignment DoF at once, all correlations taken into account 6 DoF per module considered, requires handling and solving of 35k 35k matrix Local χ 2 : similar to global χ 2, but inversion of 6x6 matrix per module 6 DoF per module, needs iterations to bring in inter-module correlations Robust Alignment: Uses only hits in overlapping modules Tracks 2-3 DoF, needs iterations, no minimization Digits Reconstruction Alignment Algorithm Iteration until convergence Align. Constants Final Alignment Constants ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 6
Global χ 2 Alignment χ 2 ansatz: Expand linearly and solve for alignment parameters For level 3 alignment all involved matrices are 35k 35k ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 7
Local χ 2 Alignment Start from global χ 2 formula Simplify by using partial derivatives instead of total derivatives (neglects inter-module correlations) and by using diagonal error matrix (neglects MCS) 35k 35k matrices break down into 6k 6 6 matrices ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 8
Robust Alignment Sum over neighbours, take correlations into account a = a i 2 / σ 2 1/ σ i i, a = x, y;i = mean residual, mean Z overlap residual, mean Rϕ overlap residual Sum over all modules in a ring mean Rϕ overlap residual z = 2π Correct for change in radius ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 9
Alignment performance: test beam Local χ 2 approach Test beam detector setup 6 Pixel & 8 SCT modules 100 GeV pions Alignment parameter x of 8 SCT modules during iterations ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 10
Alignment performance: cosmics SCT + TRT barrel test with cosmics after assembly on the surface No B-field, no momentum spectrum hardening 36k tracks used to align ~ 500 SCT modules SCT + TRT barrel cosmic test setup Robust Global χ 2 Local χ 2 ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 11
Alignment performance: cosmics SCT + TRT endcap test with cosmics Only 20k tracks useable for alignment alignment level 2 Survey information Local χ 2, level 2, residual width during iterations Survey information Global χ 2, level 2, residual width during iterations ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 12
Alignment performance: simulation Sample of 200k simulated muons Misalignment included at simulation level Global χ 2, level 3, SCT barrel residual distribution Local χ 2, level 3, only TRT misaligned, momentum resolution ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 13
Conclusion 3 track-based alignment algorithms for the ATLAS Inner Detector successfully developed Alignment of 35k DoF is a challenging task Tests with data and simulation look very promising Acknowledgements Many thanks to the ATLAS inner detector alignment group ACAT 2007 Roland Härtel MPI für Physik Alignment of the ATLAS Inner Detector 14