M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Alignment of the HERA-B Vertexdetector M. Bräuer MPI für Kernphysik, Heidelberg HERA-B and its Vertexdetector The data Coarse Alignment Fine Alignment Method External Parameters The System Results Summary

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker HERA-B: Physics I Weak, charged currents in SM : Wolfenstein : Unitarity i.e :

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker HERA-B: Physics II The  -  -plane :

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker HERA-B: Physics III

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker HERA-B: Detector I

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker HERA-B: Detector II

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker The HERA-B Vertexdetector The HERA-B Vertexdetector : Part of a multi - particle spectrometer Akceptance : mrad Resolution : 10% of the B-decay-length (0,9 mm) => µm transversal Operated in vacuum Stand-alone track reconstruktion Use its tracks already on trigger-level 7+1 Superlayer 2 Moduls per superlayer/quadrant 5° stereo angle Modules: SL 4..8 :2 double - sided SL 1..3 :1 single - sided 1 double - sided Physics  The way to a system ?..

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Detector Modules p + All quadrants of SL 1..3 : Mounted on one ‚pot‘

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Positioning of the Pots => Vertexdetector, with 32 movable axes! 4 manipulator layers, 4 quadrants, 2 Axis => System working! (MPI-K) Radial for beam injection Lateral to equalise the radiation load Movements:

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Support Pots and caps in UHV beam-pipe:  A nasty cavity for the proton beam  Shielding (flex-beam-pipe)

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker The Vertexdetector System Much additional fun with: DetectorsMPI-M UHVMPI-K & DESY Cooling MPI-K Mechanics integration MPI-K & DESY Readout chipsMPI-K, IHEP (ASIC-lab) ElectronicsMPI-K !! Slow – controlMPI-K

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Data from the VDS The signals we get are improving with time S/N Occupancy

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Data from the Full System S/N Occ. raw cleaned

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Correlations See ‚tracks‘ without an alignment and a tracking :

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Fits to Correlation Histograms Learning more?? - Reduce combinatorical background - Get an initial guess - Use non-gaussian statistics - Do the minimization  It is possible to fit ! ( General C++ class for linear functions in these histos! )

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Tracking in the Silicon Align: u - coordinate z - coordinate Stereo – angle Future: Interstrip - distance =>Sophisticated algorithms: Cellular automaton (MPI-M, default) Kalman filter: Have a track candidate ! Follow this trough the system Confirm with further hits $ Momentum  Only straight tracks Occupancy: 5%  process - noise Parameters of each module Kalman  Solve the least squares problem for a given hit association !

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Tracking with a Kalman Filter 1. Seed combinations => full combinatorics 2. Follow trough the system 3. Easy way to include additional infor- mation on the way (scattering)  An economic way to rewrite the linear least squares problem ! No magic inside

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Coarse Alignment Knowledge of module - positions:  2 mm  Alignment system has two steps ! Coarse Alignment: Only u-coordinate Basic: Do tracking in a subset, compute residuals of tracks wrt. non contributing modules! For tracking: Two Pairs of double - sided modules known & fixed! -Fix one seeding combination (Two double - sided Modules in different pots) -Use full combinatorics with a mild (  10 mm) Target cut -Compute residuals wrt. the hits on the remaining modules in the two pots - Move modules to center residual-distributions: Continue with iterations..

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Coarse Alignment II

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Coarse Alignment III A nasty problem remains: Finding the signal in the distributions! Remainder: Residuals = All tracks wrt. to all hits ! Solution: - Compute combinatorial background from measured occupancies - Subtract background from signal-histo - Search for Median or mean of rising/falling edge Problems: part b.): When to reject due to insufficient peak? part c.): Double peak due to other dgf. part f.): Peak – finding? System is semi-automatic (may ask for input)

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Fine Alignment Simultanous alignment of the full system Measured coordinate, rotation, longitudinal shift  All modules have to contribute to the tracking  Alignment has to cope with the bias of the track- parameter due to non-aligned modules. Linear least squares:  This is a „non-small matrix“ O(90 GByte) Solve the problem by exploiting its structure: Needed: Alignment- and trackparameter  Transformations of all modules, which can not be measured!  „dead“ modules  proper treatment ! =>Method by V. Blobel (H1, Uni HH)

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker External Parameters I A simple model for tracking / alignment: Parallel tracks Reality (not known)Measured: Measurements in local coordiante system: Problem underdetermined!  A movement along the COG can not be detected  Matrix can not be inverted  „External Parameters“

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker External Parameters II Solutions: Blobel Method: Numerical treatment (forget about pivot-0 part of the matrix) Assume some positions as known Optimal results: Singular-Value-Decomposition Used: Constraint the matrix with eigenvektors from SVD On the second glance: Each cut in the ‚Zylinder‘ wich is non-parallel to the axis can be used Math: The covariance - ellipsoid degenerates to a ‚Zylinder‘!

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Towards reality.. Due to Missing momentum info, noise, process-noise: Shape of the residual distribution is non gaussian! (Requirement for lin. least. squares not fulfilled)  Unbiased residuals = explicit exclusion of hit under investigation for track - fit Solution: - Additional iterations (Cut on hits in the tails) - Measure the local hit- resolution meanwhile Cuts: residual resolution of plane j tolerance in iteration i

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Towards reality II This requires the determination of the individual single hit resolution of each plane: - Use the unbiased residuals - Take the (robust) Median Absolute Deviation, (scaled for the gaussian sigma)  Much easier for automatic processing than 2Gauß-fit Histogram: scMAD Points: 2Gauss - fit All residuals: f= 

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Bringing the fine-alignment to reality Blobels program is only a single part of the fine-alignment! Problems: - Linearisation - Track findung is affected by the alignment: cuts => higly non-linear! - The system needs to be programmed. - Handling of the non – gaussian tails tracking

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Results from Alignment I Noise, non-gaussian distributions: => Monte-Carlo questionable! => Get Errors from: „Bootstrap“: Dataset  Many datasets (n tracks) Draw each track number [1..n] by using a random number.

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Results from Alignment II Korrection of artificial deviations: Geometry of 2 opposite pots changed The system corrects for that ! (As for x/y-shifts)

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Results from Alignment III Future improvements ? The split-sample investigation: - Dataset 1: Event 1, 3, 5, 7, 9.. Dataset 1: Event 2, 4, 6, 8, Align dataset 1 - use result as basis to align dataset 2 Differences found: (Errors not fully under control..)

M. Bräuer MPI-K, Juni 01 Alignment of the HERA-B Silcontracker Physics, conclusions The vertexdetector of HERA-B is an unusual huge and movable system => Positioning and alignment requires quite some effort Problem of the alignment mainly solved -Unbiased residuals are needed! -Non – gaussian distributions: Doable!! Open points : -Further improvements form the rest of HERA-B (momentum – info, global alignment) -Thermal stability of our setup ? - Even better alignment algorithm ? Physics data: (Start up phase 2000) 2 Target wires 1 Month VDS fully instru- mented, operational z-Resolution : close to design !