LHC Alignment Workshop and ATLAS Alignment Overview Grant Gorfine (Wuppertal/CERN) CAT Meeting, CERN Oct 19, 2006

Outline LHC Alignment Workshop ATLAS Inner Detector Experience/Advice from other experiments Alignment in CMS ATLAS Inner Detector The alignment algorithms CTB SR1 CSC/CDC ATLAS Muon Spectrometer

LHC Alignment Workshop 1st LHC Detector Alignment workshop 2.5 days about 100 registered people focus on track based alignment follow-up workshop planed for June ’07 focus on hardware based alignment

LHC Alignment Workshop Mathematical methods Experience from other detectors Star, Babar, Zeus, H1, SLD, CDF Overview talks Infrastructure: Detector Description Tracking Software Impact of misalignment on Physics Validation of Alignment Strategy for the 4 LHC Detectors ATLAS, CMS, LHCb, ALICE

Overview of Alignment Strategies Most alignment strategies fall in two categories. Global χ2 (also called closed form, unbiased, correlated) Minimize a global χ2. d.o.f = number of wafers x 6 (CMS 100k, ATLAS 35k) Large matrix: d.o.f x d.o.f Still need a few iterations (since non-linearities) Correlations explicitly handled. Approach used by CDF, STAR, ATLAS, CMS, ALICE Local χ2 (also called iterative, biased, uncorrelated) Minimize χ2 of each wafer/rigid body d.o.f = 6: Invert many 6x6 matrices Many iterations Correlation implicitly handled through iterations Approach Used by SLD, Zeus, H1, ATLAS, CMS, LHCB, ALICE

Experience/Advice from Other Detectors Allocate adequate manpower Most complicated issues are with weakly constrained modes. Study algorithms behaviour with systematic distortions Concentrate on providing working solution rather than getting the most elegant algorithm Dont get hung up on mathematical details Most well behaved techniques will work. Robustness is important Use complementary event types and external constraints. Survey data important but ultimately use data Retaining expertise becomes a problem down the track. Software infrastructure needs to support alignment. Be prepared for the unexpected.

Testing Global Distortions idea of systematic description of residual alignments taken from BaBar create systematic set of residual alignment constants validate the alignment approaches DR DF DZ R Radial expansion (distance scale) Curl (charge asymmetry) Telescope F Elliptical (vertex mass) vertex displacement Skew Z Bowing Twist (CP violation) Z expansion

CMS Alignment

CMS - Hardware vs Track based Both ATLAS and CMS use combination of hardware and track based alignment.

CMS Alignment Strategies Silicon detector ~100k d.o.f, (ATLAS 35k) Similar Alignment Strategies Millepede (V. Blobel). Mathematically equivalent to global chi2 approach. HIP: Equivalent to local chi2 approach. Kalman Filter Technique. Update track by track. Pioneered by CMS. Still in experimental phase. Implementation now also in ATLAS No full scale test yet.

Millepede II Algorithm Original Millepede method solves matrix eqn. Ax = B, by inverting huge matrix A. Can only be done for <12000 alignment parameters New Millepede II method instead minimises |A x – B|. Requires sparse matrix. Expected to work for ~100000 alignment parameters (i.e. for full CMS at sensor level). Both successfully aligned ~12% of tracker modules using 2M Z! events. Results identical, but new method 1500 times faster! idea of systematic description of residual alignments taken from BaBar Matrix Inversion (12000x12000) (t=13h) MinRes (t=30s,1500x faster!) CMS Note 2006/011

Data Samples High pT muons from Z,W decays Cosmic Muons Rate: 20k Z! , 100k W! per day at L=2*1033 Gold plated for tracker alignment (small multiple scattering) Exploit Z0 mass constraint Cosmic Muons ~400Hz after L1 and s.a. muon reco. Beam Halo Muons ~5 kHz per side after L1 and s.a. muon Muons from J/ and inclusive B decays J/ mass constraint Min. bias, high pt hadrons from QCD events Potentially useful for pixel alignment Beam

Alignment Strategy Basic sketch: 2007: Before beams: Cosmics (+laser alignment and survey measurements) 2007: single beams add beam halo muons 2007: Pilot run, pixel detector not installed (except few test modules) Cosmics, beam halo muons add available high pt muons, tracks Initial alignment of high level strip tracker structures (layers, rods)? 2008:Two-step approach: Add Larger statistics of muons from Z,W 1. Standalone alignment of pixel detector 2. Alignment of strip tracker, using pixel as reference To be layed out in more detail …

ATLAS Inner Detector Alignment The Construction Sites Finalize CTB Alignment SR1 Cosmics CSC/CDC

Alignment Approaches Global c2 minimisation Local c2 minimisation Large matrix inversion (35k x 35k). Currently use LAPACK – no optimization for sparse matrix. Need multiple CPUS for reasonable turn around time. Recent investigation into other methods MA27 from Harwell Subroutine Library looks promising 15 mins for 36k dof. (LAPACK 1.5 days) Also investigating use of Millepede Few iterations (non linearities) Local c2 minimisation Many small matrices (6x6) Many iterations Robust Alignment Iterative method using overlap residuals for determining relative module to module misalignments Kalman Style Alignment Approach adopted from CMS. Updates alignment track by track Extension to local c2 approach

SCT – Frequency Scanning Interferometry Endcap C Barrel 842 online and simultaneous length measurements in SCT! Endcap A Optical online monitoring of the SCT geometry using a grid of interferometers Single FSI Grid Line Interferometer has a precision below 1m! Entire Grid shape can be determined to better than 10m in 3D. FSI complements the offline track alignment where the latter is not sufficiently sensitive – lowest modes of global distortions! Still work needed to understand how to combine with track based alignment. It also provides quasi real-time response to time dependent deformations. 7

TRT Algorithm similar to Silicon Global χ2 approach being developed used on 12 out of 96 TRT barrel modules so far. Aligns 3 rotations, 2 translations and a module twist Extension to include SCT modules in alignment is under way. Alignment of global structures (whole TRT barrel) with respect to SCT is possible and was done for SR1 setup Under test with CTB setup.

Silicon Alignment in CTB

CTB Alignmnet Consistent results for the 4 alignment algorithms Momentum value and resolution, Residuals, Both pions and electrons. Track parameters (not shown here) Some differences. Expected to be due to poorly constrained d.o.f. x displacement (along beam direction rotation around global z and y

View from outside towards Side A SR1 Alignment View from outside towards Side A SCT: 468 of 2112 modules ~ 1/4 of SCT barrel TRT 12 modules: 1/8 of TRT barrel 3 scintilators for trigger

SR1 Alignment Local c2 and Global c2 Local c2 : Change of residual width vs alignment iteration Global c2 : Change of residual vs alignment iteration <> 10 m σ 43 m 1st iteration <> 2 m σ 32 m Assumed module shifts of O(100-200m) Note: different scale on plots! Simulation: with perfect aligned detector  ~ 55-60m 3rd iteration

SR1 Alignment First iteration Third iteration SR1 Cosmics (real data) Correction x100

SR1 Global alignment of TRT to SCT Shifts of TRT relative to SCT from cosmic data: run Δx [mm] rot-y [mrad] rot-z [mrad] 3007 -0.290 0.277 0.254 3009 -0.289 0.293 0.226 good agreement of alignment between different runs Compare cosmic data alignment to survey done after insertion: From survey of barrel ends after insertion survey -0.300 0.221 good agreement of track alignment to mechanical survey

CSC/CDC Misalignments in CSC Simulation Level 1 (Subsystem) O(1 mm) shifts O(0.1 mrad) rot Level 2 (Si Layers/Disks) O(100 μm) shifts O(1 mrad) rotations Some Systematic Level 2 (TRT Modules) O(1 mm) systemic shifts O(0.1) random shifts Level 3 (Silicon modules) Green: Nominal SIM Blue: TRT misaligned Pink: ID misaligned in SIM. Destroys momentum reconstruction invariant mass Z→m+m-

Alignment Readiness All approaches on the way or already arrived at the point where they can align the whole silicon part of the Inner Detector Big push to get into one boat with the TRT alignment effort Full chain (from data to tracks to alignment constants to distribution of those) was executed by all approaches for CTB and cosmic setup. Ready to tackle the CDC challenge.

ATLAS Muon Spectrometer Alignment

MS Optical Alignment Layout EO Bar Projective Polar Proximity Praxial EM BOL BML BIL EE Barrel EI + Chamber Deformations EndCap

Toroid release Release day 1 Release day 2 Optical alignment found consistent with calculation and survey Optical (ASAP): 17.6 mm Survey: 17 mm Predicted (finite element): 18 mm

Software for Muon Optical Alignment Sensor parameter to chamber position, orientation and deformation converter Image to parameter converter Monitoring PVSS Barrel Asap (Barrel) CDB Condition database Endcap PVSS Aramys (Endcap) Temperature PVSS Reconstruction Chain fully implemented at the H8 testbeam. Florian Bauer, 4/9/2006, LHC Alignment Workshop

Muon Alignment The alignment of the Atlas muon spectrometer should be known at 30μm Based mainly on optical sensors Large hardware and software developments Succeeded validations test beam toroid release Part of the alignment is based on tracks In particular some parts not covered by optical systems Straight tracks for the commissioning started to be understood at test beam Tracks in B field during normal operation complete problem to be investigated

Combined Muon and Inner Detector Activity just starting. First combined muon and inner detector alignment meeting yesterday

Summary LHC Alignment Workshop successful. Inner Detector Alignment Need to focus on Data preparation. Test alignment strategies with global distortions. Many similarities with CMS Inner Detector Alignment CTB: Alignment algorithms giving consistent results. Some degrees of freedom not well constrained. SR1: Alignment algorithms successfully being used. Gives some indication of what we can expect from cosmics. SCT/TRT alignment in good agreement with survey. CSC/CDC: Alignment group feels ready for the challenge Much work ahead to understand data sets needed. Need to understand how to combine FSI and track based alignment information. Muon Spectrometer Mainly hardware based alignment Validation with toroid release and test beam. Track based alignment – still much to do. Combined Muon/ID Work being initiated.