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

2. 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

3. 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

4. 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

5. 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

6. 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.

7. 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

8. CMS Alignment

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

10. 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.

11. 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 ~ 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

12. 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

13. 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 …

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

15. 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

16. 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

17. 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.

18. Silicon Alignment in CTB

21. 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

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

23. 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( m)
Note: different scale on plots!
Simulation: with perfect aligned detector  ~ 55-60m
3rd iteration

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

25. 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

26. 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-

27. 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.

28. ATLAS Muon Spectrometer Alignment

29. MS Optical Alignment LayoutEO
Bar
Projective
Polar
Proximity
Praxial EM
BOL
BML
BIL EE
Barrel EI
+ Chamber Deformations
EndCap

30. 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

31. 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

33. 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

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

35. 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.