LHCb Detector Alignment with Tracks NIKHEF Jamboree 2008 Artis Amsterdam Wouter Hulsbergen (BFYS)
Detector alignment LHC silicon detectors provide <20 micron coordinate resolution resolution of a point inside a silicon wafer challenge: maintain such resolution in structures that contain many wafers requires accurate positioning of detector elements, both active (when installing) and passive (in software) alignment is the procedure that calibrates detector positions input to the alignment survey: a measuring rod, RASNIK,... tracks: reconstructed trajectories from charged particles in this talk track based alignment by minimizing a chi square alignment of LHCb detector with first data 2
Tracks and residuals x z detector plane hit: strip/wire/pad with fixed coordinate x track model, e.g. x(z) = a0 + a1 z track fitting and alignment is all about hit 'residuals' track parameters 3
Track fitting x z the track fit is a 'least squares estimator' minimizes track 'chi square' 'minimize' means minimization performed with (semi ) analytic method Newton Raphson method for finding the 'zero' of a non linear function it is not so different from what's happening inside MINUIT 4
Perfect detector: residuals are unbiased x z x_hit x_track residual RMS ~ detector position resolution multiple scattering etc 5
Misaligned detector: biased residuals x z x_hit x_track note: one layer was misaligned but next layer has biased residuals as well typical problem in detector alignment: residuals from track fit are correlated 6
Alignment using residuals simple alignment method: extract misalignments from residual histograms not easy to extend to detector displacements other than measurement direction no straightforward method to deal with correlations, especially in 'segmented' detectors tracks constrain correlated movements alignment becomes a bookkeeping problem: 'residuals in module A1' with respect to tracks in B1, C2, D3' etc most popular solution: 'minimum chisquare method for alignment' consider the chi square of a sample of tracks minimize this chi square simultaneously with respect to alignment parameters and track parameters 7
Minimum chi square method for alignment the solution to this minimum chi square problem can again be written as change in alignment parameters correlations between elements 'the big matrix' 'the big vector' average residuals eliminating the track parameters from this problem is actually not totally trivial need to exploit that different tracks only correlated via alignment parameters best known implementation of this idea: MILLIPEDE by Viktor Blobel 8
Weak modes: poorly constrained common movements special complication in alignment with tracks: some (linear) combinations of alignment parameters are unconstrained global translation z scale shearing more dangerous than unconstrained modes are so called 'weak modes' 'statistically underconstrained' common movements in a track samples with finite size extremely sensitive to mistakes ('outliers') in track reconstruction can lead to poor convergence of alignment procedure weak modes are the major concern in detectors that require alignment of many elements LHCb inner tracker: silicon tracker with O(500) ladders LHCb outer tracker: drift chamber with 216 modules CMS/Atlas inner detectors 9
Example of unconstrained mode in LHCb spectrometer LHCb spectrometer measures 'kink' of particle around magnet axis: kink Q/pxz shearing of the tracking stations leads to bias in the kink momentum bias velo TT magnet forward tracker shearing Q/p bias 10 m J/psi mass peak versus p( +) p( ) Analysis of Eduard Simioni: shearing bias in mass as function of asymmetry of decay can be used to extract shearing with <100 micron precision from J/psi + decays 10
Amoraal Raven LHCb Alignment Framework main idea (Jan Amoraal, Gerhard Raven): use the fact that all LHCb detectors implement alignment correction in the same way are used by track fit in the same way developed a single framework that can align all tracking detector simultaneously runs inside the standard LHCb reconstruction framework no separate n tuples, root macros,... uses the standard LHCb track fit, which is a Kalman filter multiple scattering corrections proper integration of magnetic field use in alignment requires small extension of K filter math (see arxiv:0810.2241) work relies on NIKHEF expertise in LHCb geometry and track fit Jeroen van Tilburg, Eduardo Rodrigues, Juan Palacios, Edwin Bos, framework extensively tested on MC 11
Alignment efforts with first real data CMS ATLAS VELO (Si strip) TT (Si strip) OT (straw tube) IT (Si strip) MUON (pads) two sources of tracks in 2008 tracks from LHCb beam dump ('TED'), used for alignment of silicon detectors tracks from cosmic muons, used for alignment of Outer Tracker 12
Data sample 1: beam dump muons from the 'TED TED: beam dump at end of injector, about 300 m from LHCb two separate data sets with about 700 tracks each not all detectors operational: only VELO, TT, IT (+CALO for trigger) relatively high track density: hard for tracking in TT and IT ('long strips') 13
VELO tracks in TED run tracks hits on tracks other hits direction of TED muons hits per track tracks parallel to beam traverse many layers good for alignment 14
VELO alignment correction to survey extracted from alignment with tracks 20 micron good agreement of alignment taken from 2 different data sets mm VELO single hit resolution versus strip pitch VELO hit resolution still a bit larger than expectation but: unknown contribution from multiple scattering magnet off no momentum measurement survey only after alignment line: binary resolution mm 15
Velo TT/Velo IT alignment VELO tracks also seen in other silicon tracking systems VELO TT extrapolation over about 1.5 m survey alignment better than 500 micron VELO IT extrapolation over about 7 m IT survey has 'mm' uncertainties 16
Data sample 2: cosmics preferred direction of cosmic muon not a great match! preferred direction of LHCb 17
Bauer Merk Pellegrino proposal proposal to improve acceptance includes study to find optimal angle proposal didn't make it despite this >2 M triggered cosmic events mainly HCAL/ECAL ~50k OT tracks >5k OT MUON tracks important for OT, MUON, commissioning 18
Cosmic event OT hits ECAL HCAL MUON hits #OT hits on reconstructed OT segments 19
Debugging OT with cosmics data OT module has two mono layers, relative offset ½ cell size in x z ½ cell space x analyzing first data, Jan found we had swapped two mono layers in readout map but when he fixed it, alignment became even worse! (ignore error bars, they are wrong) very puzzling: even prompted Marcel to run his own reconstruction as cross check it turned out we had also put the ½ cell size spacing in the wrong mono layer 20
Alignment algorithm at work: OT layers and modules (half)layer level alignment displacements up to 2mm from expected position most likely cause: another error in the OT description in software 1 half layer = 9modules module level alignment displacements up to 1mm from average in layer a bit larger than expected from mechanical tolerances 21
OT tracks extrapolated to ECAL and MUON OT ECAL ~2.3cm ~4.7cm ~5.6cm OT MUON 'correlation plots' used for first rough alignment and finding problems in geometry work on simulation in progress in order to understand resolution 22
More OT analysis: space drifttime calibration 'rt' calibration: extract relation between measured drifttime and track position drift time spectrum unbiased distance vs drift time Alexandr Kozlinskiy Thomas Bauer tdc offset calibration yields valuable information on 'mis configured' electronics 23
Summary LHCb has implemented a state of the art alignment algorithm for its tracker can align all components of tracking system: VELO, TT, IT, OT and MUON uses standard LHCb track fit analysis of tracks in first data is in full swing TED data for alignment of VELO, TT, IT detectors cosmics data for OT and MUON NIKHEF BFYS group is well represented in this project geometry track fit velo alignment OT alignment and calibration 24