28 06 2001 M Bruer MPI fr Kernphysik

28. 06. 2001 M. Bräuer MPI für Kernphysik, Heidelberg Alignment of the HERA-B Vertexdetector • HERA-B and its Vertexdetector • The data • Coarse Alignment • Fine Alignment • Method • External Parameters • The System • Results • Summary M. Bräuer Alignment of the HERA-B Silcontracker MPI-K, Juni 01

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

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

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

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

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

The HERA-B Vertexdetector : • Part of a multi - particle spectrometer • Akceptance : 10. . 250 mrad • Resolution : 10% of the B-decay-length (0, 9 mm) => 20 - 30 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 Alignment of the HERA-B Silcontracker MPI-K, Juni 01

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

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

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

The Vertexdetector System Much additional fun with: • Detectors • UHV • Cooling • Mechanics integration • Readout chips • Electronics • Slow – control M. Bräuer MPI-M MPI-K & DESY MPI-K, IHEP (ASIC-lab) MPI-K !! MPI-K Alignment of the HERA-B Silcontracker MPI-K, Juni 01

Data from the VDS S/N The signals we get. . 1998 are improving with time. 2000 Occupancy 1998 2000 M. Bräuer Alignment of the HERA-B Silcontracker MPI-K, Juni 01

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

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

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

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

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

Coarse Alignment Knowledge of module - positions: 2 mm Þ 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 Alignment of the HERA-B Silcontracker MPI-K, Juni 01

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

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 Alignment of the HERA-B Silcontracker MPI-K, Juni 01

Fine Alignment • Simultanous alignment of the full system • Measured coordinate, rotation, longitudinal shift Þ All modules have to contribute to the tracking Þ Alignment has to cope with the bias of the trackparameter due to non-aligned modules. Needed: Alignment- and trackparameter Linear least squares: ÞThis is a „non-small matrix“ O(90 GByte) Solve the problem by exploiting its structure: => Method by V. Blobel (H 1, Uni HH) • Transformations of all modules, which can not be measured! Þ proper • „dead“ modules treatment ! M. Bräuer Alignment of the HERA-B Silcontracker MPI-K, Juni 01

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

External Parameters II Math: The covariance - ellipsoid degenerates to a ‚Zylinder‘! On the second glance: Each cut in the ‚Zylinder‘ wich is non-parallel to the axis can be used 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 M. Bräuer Alignment of the HERA-B Silcontracker MPI-K, Juni 01

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) Þ Unbiased residuals = explicit exclusion of hit under investigation for track - fit Solution: - Additional iterations (Cut on hits in the tails) - Measure the local hitresolution meanwhile Cuts: residual M. Bräuer tolerance in iteration i Alignment of the HERA-B Silcontracker resolution of plane j MPI-K, Juni 01

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) Þ Much easier for automatic processing than 2 Gauß-fit Histogram: sc. MAD Points: 2 Gauss - fit All residuals: f= M. Bräuer 100 Alignment of the HERA-B Silcontracker 10 MPI-K, Juni 01

Bringing the fine-alignment to reality tracking 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 M. Bräuer Alignment of the HERA-B Silcontracker MPI-K, Juni 01

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 Alignment of the HERA-B Silcontracker MPI-K, Juni 01

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 Alignment of the HERA-B Silcontracker MPI-K, Juni 01

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, 10. . - Align dataset 1 - use result as basis to align dataset 2 Differences found: (Errors not fully under control. . ) M. Bräuer Alignment of the HERA-B Silcontracker MPI-K, Juni 01

Physics, conclusions Physics data: (Start up phase 2000) 2 Target wires 1 Month VDS fully instrumented, operational z-Resolution : close to design ! • 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 ? M. Bräuer Alignment of the HERA-B Silcontracker MPI-K, Juni 01