Alignment of the Inner Detector using misaligned CSC data

Transcription

1 Alignment of the Inner Detector using misaligned CSC data J. Alison 1, A. Bocci 2, O. Brandt, P. Bruckman de Renstrom, B. Cooper 4, M. Elsing 5, C. Escobar 6, D. Froidevaux 5,. Golling 8, S. González-Sevilla 6, F. Heinemann, M. Karagöz Ünel, V. Lacuesta 6, S. Martí i García 6, R. Moles 6, A. Morley 7, S. Pataraia 9, J. Schieck 9, C. Schmitt 5 1 University of Pennsylvania, Department of Physics & Astronomy, 29 S. rd Street, Philadelphia, PA 1914, United States of America 2 Duke University, Department of Physics, Durham, NC 2778, United States of America Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 RH, United Kingdom 4 Queen Mary University of London, United Kingdom 5 CERN, CH Geneva 2, Switzerland, Switzerland 6 Instituto de Física Corpuscular (IFIC), Centro Mixto UVEG-CSIC, Apdo. 2285, ES-4671 Valencia; Dept. Física At., Mol. y Nuclear, 7 School of Physics, University of Melbourne, Victoria 1, Australia 8 Lawrence Berkeley National Laboratory and University of California, Physics Division, MS5B-6227, 1 Cyclotron Road, Berkeley, CA 9472, United States of America 9 Max-Planck-Institut für Physik, (Werner-Heisenberg-Institut), Föhringer Ring 6, 885 München, Germany September 5, 28 Abstract An important milestone within the Computing System Challenge (CSC) was the production of a set of alignment constants for the Inner Detector using a data sample generated with the CSC misaligned geometry. For this the Pixel detector together with the Semiconductor racker were first aligned internally using a method based on the minimization of hit residuals. he R was then aligned with respect to the Pixel and the SC using a similar approach. A collection of observables, some using Monte Carlo truth information, were used to validate the results. he set of constants obtained was used for the results presented in the ALAS detector paper. 1

2 Contents 1 Introduction 2 Data Sample 2.1 he Multimuon sample he cosmic ray sample Internal alignment of the Pixel and SC 6 4 Alignment of the R with respect to the Pixel and SC 9 5 Performed cross-checks 1 6 Validation of the Alignment 16 7 Summary and Outlook 19 A Inner Detector misalignments for CSC 21 A.1 Silicon misalignments for CSC A.1.1 Silicon: Level 1 transforms A.1.2 Silicon: Level 2 transforms A.1. Silicon: Level transforms A.2 R misalignments for CSC A.2.1 R: Global transform (Level 1) A.2.2 R: Module level transform (Level 2) B Error Scaling 24 2

3 1 Introduction he Computing System Challenge (CSC) was an important milestone towards data taking with the ALAS experiment at the LHC. For this a large scale production of simulated data based on a misaligned geometry [1] was produced. A subset of these events was used to produce a set of alignment constants estimating the expected alignment performance in the ALAS detector paper [2]. In addition several analysis were repeated with these set of alignment constants containing residual misalignments. he introduced deformations were based on the expected uncertainty during the construction of the various detector components, leading to movements up to several millimeters. he misalignment did not take into account possible improvements based on survey measurements and this misaligned geometry is referred as as-built-geometry. First alignment exercises of the SC using tracks from cosmic rays indicate, that the observed misalignment might be smaller that the introduced one for this exercise (see appendix A and []). he misalignment contained only a limited number of systematic deformations like a sagitta effect based on the movement of a complete Silicon barrel layer and a clocking effect from a systematic rotation of the Silicon barrel layers, leading to biased measurements of the momentum. Systematic deformations which can be described by coherent movements of particular modules, like a twist or an elliptical deformation, were not introduced. At the module level only random misalignments were introduced. Section 2 summarizes the event sample used to determine the constants, Section explains the alignment of the Silicon part and Section 4 the alignment of the R. Section 5 summarizes performed cross-checks, Section 6 describes the validation of the set of constants obtained and Section 7 summarizes the results. Finally, there are two appendices, one with the CSC misalignment numbers for the Inner Detector (ID) and another one with the numbers for the error scaling used during the alignment procedure. 2 Data Sample 2.1 he Multimuon sample he multimuon sample consisted of almost 1 5 events produced using the full ALAS simulation chain. he simulation and digitization jobs ran on the GRID using AHENA release he sample was generated as one of the ID calibration samples of the CSC exercise with run number 727. he multimuon events have been simulated with the geometry tag ALAS-CSC-1-2- with distorted materials for the ID and LAr impplemented, a magnetic field 1 with initial displacements and the misaligned geometry (CSC misalignments for the ID can be seen in the appendix A, further details are given in [1, 4]). Each event contained 1 muons with all muons possesing the same charge. All tracks originated from the same point using the generated position of the first particle, which corresponded to the primary vertex of that event. Positively and negatively charged muons alternated from one event to the next. he track parameters p,ηandφfor the muon tracks were choosen to be flat with the following track parameter ranges: he transverse momentum spectrum range is p = [2, 5] GeV/c. he pseudorapidity range is η = [-2.7, 2.7] he azimutal angle range is φ = [, 2π] Overall almost 1 million tracks were simulated. he distributions of the truth track parameters are shown in figure 1. the sample can be found in CASOR: Main directory: /castor/cern.ch/grid/atlas/dq2/misal1 mc12/ Subdirectory: misal1 mc multimuonsgeneration.digit.rdo.v1212 tid678

4 rk::rack ruth Parameter: d Entries rk::rack ruth Parameter: z Entries rk::rack ruth Parameter: phi Entries Mean 2.761e-5 Mean Mean RMS RMS RMS Underflow 1 Underflow 1 Underflow Overflow 1 Overflow 16 Overflow d (mm) z (mm) φ (rad) rk::rack ruth Parameter: theta Entries rk::rack ruth Parameter: eta Entries rk::rack Parameter: p/q Entries Mean 1.57 Mean.7597 Mean RMS RMS RMS Underflow Underflow Underflow Overflow 12 Overflow Overflow θ (rad) η = -ln (tan(θ/2)) p/q (GeV/c) Figure 1: ruth track parameters of the multimuon sample. he primary event vertex distribution was generated using a gaussian distributions centered around zero with a width of (see figure 2): transverse plane (v x and v y ):σ= 2 15µm along the beam axis (v z ):σ= 2 56 mm Figure 2 show see the generated distributions for each vertex coordinate (top plots) and the correlations between the the coordinates (bottom plots). 2.2 he cosmic ray sample For the alignment of the misaligned detector two different kind of cosmic samples were. In both cases, the simulation was performed considering that the ALAS detector is located in the cavern and the misaligned CSC geometry was used. he first sample was simulated without magnetic field and the second one with the ID solenoidal B-field simulated. For the generation of these samples, the CosmicGenerator constrained the production vertex and track direction at generator-level. herefore the events samples consisted only of cosmic tracks contained within the inner detector volume. his filtering task was performed by the G4CosmicFilter requiring simulated hits inside a certain volume (the ID in these cases). In the following lines both samples are described. 1. he first sample was generated without magnetic field (NoBF sample). wo samples with different filter volumes were produced: (a) R barrel volume as filter 1 Using bmagatlas4 test1.data magnetic field description file 4

5 Entries Generated Particle Vertex X Position Entries Generated Particle Vertex Y Position Entries Generated Particle Vertex Z Position Entries Mean 1.668e-5 Mean Mean RMS RMS RMS Underflow 1 Underflow Underflow 1 6 Overflow 1 6 Overflow 2 Overflow 5 Entries 5 Entries genparticle Vertex X Position (mm) genparticle Vertex Y Position (mm) genparticle Vertex Z Position (mm) genparticle Vertex Y Position (mm) genparticle Vertex X Vs Y Pos Entries Mean x 1.668e-5 Mean y RMS x RMS y genparticle Vertex X Position (mm) genparticle Vertex X Vs Z Pos Entries Mean x Mean y 1.667e-5 RMS x RMS y genparticle Vertex Y Position (mm) genparticle Vertex Y Vs Z Pos Entries Mean x Mean y RMS x RMS y genparticle Vertex X Position (mm) genparticle Vertex Z Position (mm) genparticle Vertex Z Position (mm) Figure 2: Generated vertex distribution of the multimuon sample. he geometry tag used was ALAS-CommNF-2-- which has the same geometry as the multimuon sample (ALAS-CSC-1-2-). 87k events were available at this time for this sample, with about 2k silicon tracks. he sample was produced with release 1..1 and can be found here: /castor/cern.ch/user/l/lytken/cosmic 11/digitization/NoField/RBarrel/misaligned/ (b) SC barrel volume as filter he geometry tag used was ALAS-CommNF-2-- as the previous one. 15k events were available at this time for this sample, with about 1k silicon tracks. his sample was produced with release 1..2 and can be found here: /castor/cern.ch/user/j/jboyd/cosmic 12/digitization/NoField/SCBarrel/misaligned/ he only difference between these two samples was the track efficiency, 26% for the R volume filtered tracks and 6% for the SC volume filtered sample. As the cosmic sample was used in the silicon alignment to contraint some weak modes, the use of the SC barrel volume saved a lot of processing time. Figure shows the truth generated parameter for the latter case. Note, thatφ peaks around -π/2 which means that cosmic rays were coming mainly from the zenith.θ (orη) shows two peaks corresponding to the cavern s shafts. Finally, the bottom right plot shows a null momentum distribution as the magnetic field was not present. 2. he second sample was generated with the magnetic field on (BF sample). Just one sample with the R Barrel Volume as filter was produced: he geometry tag used was ALAS-Comm-2-- which has the same geometry as the multimuon sample (ALAS-CSC-1-2-). 17k events were available at this time for this sample, with about 4.5k silicon tracks. 5

6 rk::rack ruth Parameter: d Entries 9942 rk::rack ruth Parameter: z Entries 9942 rk::rack ruth Parameter: phi Entries 9942 Mean Mean Mean RMS RMS RMS.422 Underflow 26 4 Underflow Underflow Overflow 4 Overflow 9 16 Overflow d (mm) z (mm) φ (rad) rk::rack ruth Parameter: theta Entries 9942 rk::rack ruth Parameter: eta Entries 9942 Parameter: p/q rk::rack Entries 9942 Mean 1.66 Mean Mean 1 RMS.4497 RMS RMS Underflow Underflow 12 Underflow Overflow 8 Overflow Overflow θ (rad) η = -ln (tan(θ/2)) p/q (GeV/c) Figure : ruth track parameters of the cosmic NoBF sample (SC Barrel volume filter). he release used to generate this BF sample sample was his sample was produced with release 1..1 and can be found here: /castor/cern.ch/user/l/lytken/cosmic 11/digitization/RBarrel/misaligned/ As in the previous case, the track efficiency is 26% for the R Barrel volume filtered tracks. Figure 4 shows the truth track parameters for this BF sample. Again, the cavern s shafts and the cosmic rays direction, coming from the zenith, can be respectively seen in theθ (orη) andφ distribution. he momentum distribution divided by the particle charge p/q in the right bottom plot shows that the magnetic field was switch on in the simulation. Please note the asymmetry between the number of positively and negatively charged tracks in the p/q. his asymmetry originates from the CosmicGenerator due to the fact that protons (positively charged particles) were used to generate these cosmic events and therefore the charged distribution is biased towards positive particles. Internal alignment of the Pixel and SC he ID alignment procedure started with the internal alignment of the silicon detectors (Pixel and SC). he Globalχ 2 algorithm [5] was run iteratively starting from the fully misaligned geometry, i.e. using the nominal geometry description (COOL database tag: OFLCOND-CSC---) as defined for the CSC exercise [1] and using the multimuon simulated events as described in 2.1. were processed independently from one another (no common vertex option used). For all iterations tracks with momenta above 1 GeV/c were constrained to be consistent with the beam line assumed at (,) in the XY plane. he constrained used was soft, i.e. the tracks were constrained to the beam line with an error 1 times larger than the error on their transverse impact parameter (d) obtained from the track fit. he iterations can be divided in three phases: 6

7 rk::rack ruth Parameter: d Entries 589 rk::rack ruth Parameter: z Entries 589 rk::rack ruth Parameter: phi Entries 589 Mean Mean.15 Mean RMS RMS 64. RMS.4796 Underflow 12 Underflow Underflow 22 Overflow 17 2 Overflow 6 7 Overflow d (mm) z (mm) φ (rad) rk::rack ruth Parameter: theta Entries 589 rk::rack ruth Parameter: eta Entries 589 rk::rack Parameter: p/q Entries 589 Mean Mean Mean Overflow 5 Overflow Overflow 279 RMS.4429 RMS.4848 RMS.145 Underflow Underflow Underflow θ (rad) η = -ln (tan(θ/2)) p/q (GeV/c) Figure 4: ruth track parameters of the cosmic BF sample (R Barrel volume filter). 1. Initial four iterations involving the degrees of freedom (DoF s) of barrel cylinders and end-cap discs all considered as rigid objects (6 DoF s per object) were performed. his corresponds to, so called, Level 2 of the hierarchical geometry description of the ID (see appendix A and [1, 4]) with 186 DoF. he processing used the triangular implementation of the symmetric matrix (AlSymMat) and the solution was obtained by means of diagonalisation (SolveOption=1) with the first four eigen-modes removed. hese should correspond to the (only) four near-singular modes of the solution, i.e. the three rotations and the translation along Z of the whole system. Note, that the freedom of the X and Y translations have been removed by the beam line constraint. 2 he iterations used 1, multimuon events each ( 1, muon tracks). 2. wo iterations involving, so called, Level i.e. the entire set of 4,922 DoF s of the ALAS silicon system. his step used the sparse representation of the symmetric matrix (AlSpaMat) and the solution was obtained using the MA27 direct fast solver (SolveOption=2). Limited statistics of the tracks and the solving method imposed the necessity of matrix preconditioning. Direct solvers cannot deal with ill-defined or explicitly singular problems. Moreover, without diagonalisation one has no control over the statistical error of the solution. In order to overcome these difficulties a soft mode cut was introduced. Mathematically, it was equivalent to introducing penalty terms in theχ 2 limiting the magnitude of the individual DoF corrections. he assumed constraint corresponds closely to the allowed statistical error on the correction. he soft cut values (motivated by the CSC misalignments themselves) with self-explanatory joboption flag names are in table 1: Which meant that e.g. we did not accept any modes leading to error on the local X corrections in Pixels larger than 1µm. Later these constraints were increased by factor ten for the sake of conservativeness, resulting in slightly compromised alignment quality. he latter were e.g. published 2 his procedure is not fail safe as some degenerate modes may sneak in and distort the expected eigen-spectrum. A safer recipe consists of explicit elimination of the singular modes. Lagrange Multipliers orχ 2 penalty terms will be used in the future. 7

8 SoftPIXXerror=.1 mm SoftPIXYerror =.1 mm SoftPIXZerror =.15 mm SoftPIXRXerror=. rad SoftPIXRYerror=. rad SoftPIXRZerror=. rad SoftSCXerror=.5 mm SoftSCYerror =.5 mm SoftSCZerror =.5 mm SoftSCRXerror=. rad SoftSCRYerror=. rad SoftSCRZerror=. rad able 1: Soft Cut values used in the CSC alignment exercise in the performance chapter of the ALAS Detector paper. Each iteration used 5, multimuon events ( 5, muon tracks).. Final two iterations of the Level 2 alignment. he configuration of these iterations was identical to the one of the first four. he purpose of this last step was two-fold: align out any residual distortions that might have been introduced by the Level iterations and confirm the convergence. In reality these two iterations returned nearly negligible corrections. his observation confirmed our assumption about the Level alignment using the soft mode cut technique. By construction Level was designed to provide correction of local misalignments only (high spacial frequency strong eigen-modes). For the Error Scaling (see appendix B for description) the IndetrkErrorScaling rel1 tag was used (for more details, see table 7 for the values) for all eight iterations. he Newracking and the GlobalChi2Fitter were used to reconstruct and fit tracks in the Inner Detector. were reconstructed and fitted with silicon hits only. he described procedure above was not designed to remove multiple weak modes of the system. Such are inherently irreducible with any algorithm based on interaction tracks only [6]. In order to remove the certain weak distortions additional information provided by the simulated cosmic muons was used. he above eight iterations were, therefore, appended with one more iteration at level 2 which combined the 1, multimuon events with the simulated cosmic muons (see section 2.2). he corresponding eigenvalue spectrum is shown in figure 5. he multimuon sample was processed with exactly the same setup as the other Level 2 iterations except tracks were reconstructed and fitted without the error scaling. he cosmic events were processed using the same alignment settings as for the multimuons except the d constraint was removed. he two samples ( multimuons and cosmics) were processed separately and their resulting matrix and vector were added together before solving the system using the big add standalone program included in the SiGlobalChi2Algs package. he final corrections were obtained by diagonalizing and solving the combined matrix and vector. Cosmic events are reconstructed predominantly in the barrel and this is where a significant improvement of the reconstructed track parameters due to use of cosmic events was observed. he main iteration sequence and all of the multimuon processing was done using Athena release and the alignment software which was archived in the following branch tags: InDetRecExample (steering package to run ID reconstruction and alignment) InDetAlignGenAlgs (data and geometry preparation for the Globalχ 2 algorithm) SiGlobalChi2Algs (the main Globalχ 2 algorithm) s over Level 2 and Level alignment were executed using the GlobalChi2 CSC cycle.sh shell script which can be found in theshare folder of the SiGlobalChi2Algs he cosmic events with and without B-field were reconstructed and processed in the Athena release 1..2 and the following software tags: InDetCosmicRecExample--25 (steering package to run ID cosmic reconstruction and alignment) Notably the global sagitta, curl and the telescope weak modes can be efficiently removed this way. 8

9 eingenvalue DoF: 186 eigenmode DoF < mode mode Figure 5: Eigenvalue spectrum, including error bars for the first 18 modes. InDetAlignoolInterfaces---2 (interface classes for the ID alignment algorithms and tools) InDetAlignrkInfo--1- (Alignrk class definition) InDetAlignGenools (common tools for storing alignment constants in the DB, etc) InDetAlignGenAlgs--1-4 (data preparation for the Globalχ 2 algorithm) SiGlobalChi2AlgebraUtils---7 (Globalχ 2 algebra classes) SiGlobalChi2Alignools---22 (Globalχ 2 tools such as geometry preparation, etc) SiGlobalChi2Algs (the main Globalχ 2 algorithm) wo different samples of simulated cosmic events were used and merged together with the multimuon sample: without and with the magnetic field inside the ID. Both gave qualitatively the same results. For both cases, the alignment corrections were stored in the COOL database, with the following tags: Multimuons + NoBF cosmics (SC Volume + R Volume): OLFCOND-CSC--1-4 Multimuons+BF cosmics (R Volume): OLFCOND-CSC In the first case, for tag OLFCOND-CSC--1-4, a new set of error scaling factors were estimated and included in this tags (see table 8). In the second case, no error scaling was estimated and the nominal values (see appendix B) are used when one selects this tag from the database. 4 Alignment of the R with respect to the Pixel and SC he alignment of the R detector (barrel and endcap) was performed after the internal alignment of the Silicon, as described in the previous section, was completed. As for the silicon alignment, tracks were reconstructed with the Newracking and fitted with the GlobalChi2Fitter. However, for the R alignment, all Inner Detector hits were employed (except for a preliminary step as it will described below). heralignalgs algorithm was used for this purpose and it was executed in the Localχ 2 mode [7]. he entire procedure was performed in two phases, corresponding to the two levels of misalignment included in the CSC geometry of the R (see appendix A.2) 4 his COOL database tag was the one used for the results shown in the performance chapter in the ALAS detector paper [2]. 9

10 1. A first set of iterations were done considering the whole Barrel and the two Endcap R detectors as a rigid body, i.e. allowing only 6 Dofs each (Level 1 alignment). In practice this step is supposed to correct for the misalignment between the Silicon and the R, and among the R Barrel and Endcaps. Given the high number of R hits collected in the whole Barrel and Endcaps, a relatively small number of tracks are needed to perform this alignment step and to achieve the desired precision. In the end about 2, tracks were used. In order to minimize the bias due to the internal misalignment of the R modules (that at this stage is not taken into account), a preliminary internal alignment of the barrel modules was performed (before the L1 alignment) using R-only tracks (i.e. tracks reconstructed with only R hits). he precision that can be achieved with such R-only tracks however is not competitive with the one that can be obtained with full tracks and therefore no attempt was tried to optimize such internal alignment. he Level 1 alignment was observed to converge after about 4 iterations. 2. A second set of iterations (Level 2) were done in order to perform the internal alignment of the R. All the 96 modules in the barrel were considered as rigid body and 6 Dofs were assigned to each of them. Since the CSC misaligned geometry [1] did not include any R Endcap module displacements, they were not included in Level 2 alignment procedure. he preliminary internal alignment done with the R-only tracks were not used in this step (not even to provide a starting position for the modules). In this way the robustness of the method was tested for the case of no prior knowledge of the module position. he increase in granularity and number of Dofs required an increased number of tracks to be employed. For this Level 2 alignment about 75, tracks were used. he Level 2 alignment was observed to converge after about 8 iterations. It is important to note that, in contrast with the Silicon alignment, no cosmics were employed in the R internal alignment for this CSC exercise. All the iterations were done using the Athena release 1..4 and with the R AlignAlgs--2-1 tag of the R alignment code. he parameters of theglobalchi2fitter were set to their default value expect for the following ones: ExternalMat set torue FillDerivativeMatrix set torue CopyRIOs set tofalse OutlierCut set to. (instead of the default 5.) he track selection required at least 5 hits in the SC and at least 2 hits in the R (no requirements for Pixel hits). In fig. 6 a visualization of the R barrel module displacements are shown as they are in the CSC misaligned geometry (the reference is the ideal geometry). In fig 7 a similar visualization is shown for the residual displacement after the alignment (again using the ideal geometry as a reference). Random fluctuations of the module position are due to the finite number of hits used to align the R modules. hey can be considered as statistical fluctuation. However a systematic movement of all modules along the R φ direction were also observed. his means that the original clocking effect present in the CSC geometry has not been totally removed. he origin of suck residual clocking effect (and the possible way to reduce it) is the topic of a dedicated study reported in a separated document [8]. 1

11 translation x 5 - Layer translation x 5 - Layer 1 y [mm] 1 y [mm] mm 1 mm x [mm] x [mm] translation x 5 - Layer 2 Projection along Rφ x 1 y [mm] 1 y [mm] mm 1 mm x [mm] x [mm] Figure 6: R barrel modules displacements as they have been implemented in the CSC misaligned geometry (Level 2 only): the first three plots (from top to the bottom) show the misplacements for the three R layers in the (X,Y) plane. Each arrow represent the misplacement of a module with respect to its nominal position. As reported in able 6 they are composed by a systematic radial movement (the same for all the modules in a layer) and by random movements in the R φ direction. he projection of the modules movements in R φ are visualized in the bottom-right plot. Given the asymmetry between clockwise (blue) and anti-clockwise (red) movements, an effective clocking effect is introduced with the CSC misalignment geometry. 11

12 translation x 5 - Layer translation x 5 - Layer 1 y [mm] 1 y [mm] mm 1 mm x [mm] x [mm] translation x 5 - Layer 2 Projection along Rφ x 1 y [mm] 1 y [mm] mm 1 mm x [mm] x [mm] Figure 7: A visualization similar to fig. 6 for the R barrel module. In this case the arrow represent the displacement of the module after the R level 2 alignment with respect to the true position of the modules in the CSC misaligned geometry. he asymmetry between clockwise (blue) and anti-clockwise (red) movements implies that a residual clocking effect is still present after the R level 2 alignment. 12

13 ) -1 (GeV true /dp scale dp x (a) η <.8 x.1 x1 x1 x1 ) -1 (GeV true /dp scale dp x (b) η >1.5 x.1 x1 x1 x1 Figure 8: he differential momentum scale in (a) the central barrel and (b) end caps for silicon only tracks during Level 2 iterations with the Multimuon sample. he strength of the beam spot constraint were scaled by the amounts indicated. 5 Performed cross-checks In order to validate the obtained alignment results and check the stability of the method, various checks of the algorithm have been performed. hese can be divided into three cathegories. 1. further iterations of either Level 2 or Level alignment in order to verify the convergence of the method and lack of uncontrolled runaway. Figures 8 to 1 show that the algorithm has converged to a stable solution. 2. Level 2 alignment starting from the nominal alignment and using different error parameters for the constraint on track d. he resulting alignment constants were checked for the ability to reconstruct the beam line correctly. In particular the dependence of the reconstructed d on the track direction in the XY plane (trackφ) has been inspected in addition to the transverse impact parameters resolution. Figure 1 demonstrates that resolution of d is relatively independent of the strength of the constraint imposed.. soft mode cuts were scaled up and down in the range.1 1 in order to verify stability of the Level alignment. A plateau of workable cut values has been identified, see figures 11, 12 and 1. Convergence was slowed as the constraints are tightened while weak modes dominate the solution if the constraints are relaxed too much. Various figures of merit were used to gauge the quality of the resulting alignment. he distribution of the reconstructed track transverse momenta as well as the remaining four track parameters served as the first check. hen a comparison of reconstructed to generated track parameters gave more detailed picture. Within the latter, testing for the residual global sagitta distortion was of the primary interest. he quantity Q/p rec /Q/ptrue, which will be referred to as the momentum scale (pscale ), was ploted in the form of a profile histogram against the true signed track transverse momentum. he slope of this dependence, is a direct evidence of a sagitta distortion. Figures 8 and 11 show the effects of varying the strength of the constraints applied at level 2 and level alignment on the differential momentum scale (dp scale /dp true ). Furthermore, the mass peak of Z µ + µ was checked for it s central value and width. A charge asymmetry of tracks in the Z mass peak (N µ + N µ /N µ ++N µ ) also served as a Monte Carlo independent check of the sagitta distortion. Finally, a direct comparison of the obtained alignment corrections to the true constants introduced in the CSC geometry was done. his was used for both Level 2 and Level alignments. o ensure that the overall procedure was converging to a solution, simple checks were performed on the the residual distributions. Figure 14 shows the local x residuals for silicon only tracks in the in pixel and 1

14 =5 GeV (GeV) resolution at p p 7 x x.1 x1 x1 x1 =5 GeV (GeV) resolution at p p x.1 x.1 x1 x1 x (a) η <.8 (b) η >1.5 Figure 9: he p resolution for muons with p = 5 GeV in (a) the central barrel and (b) end caps for silicon only tracks during Level 2 iterations with the Multimuon sample. he strength of the beam spot constraint was modified by the amounts indicated. resolution (mm) d 1 x.1 x.1 x1 x1 x Figure 1: he resolution of the transverse impact parameter for silicon only tracks during Level 2 iterations the Multimuon sample. he strength of the beam spot constraint were scaled by the amounts indicated. he strength of the beam spot constraint was modified by the amounts indicated. ) -1 (GeV true /dp scale dp (a) η <.8 x.1 x.5 x1 x2 x1 ) -1 (GeV true /dp scale dp (b) η >1.5 x.1 x.5 x1 x2 x1 Figure 11: he differential momentum scale in (a) the central barrel and (b) end caps for silicon only tracks during Level iterations with the Multimuon sample. he strength of the soft cut was scaled by the amounts indicated. 14

15 =5 GeV (GeV) resolution at p p x.1 x.5 x1 x2 x1 =5 GeV (GeV) resolution at p p x.1 x.5 x1 x2 x1 (a) η <.8 (b) η >1.5 Figure 12: he p resolution for muons with p = 5 GeV in (a) the central barrel and (b) end caps for silicon only tracks during Level iterations with the Multimuon sample. he strength of the soft cut was scaled by the amounts indicated. resolution (mm) d x.1 x.5 x1 x2 x Figure 1: he resolution of the transverse impact parameter for silicon only tracks during Level iterations with the Multimuon sample. he strength of the soft cut was scaled by the amounts indicated. 15

16 Arbitrary Units.1.8 Ideal layout Misaligned layout Aligned layout Arbitrary Units.25.2 Ideal layout Misaligned layout Aligned layout x residual (mm) x residual (mm) (a) Pixel barrel (b) SC barrel Figure 14: he local x residual distribution for the barrel of the (a) Pixel and (b) SC detectors RMS of local x residual (µm) 7 Pixel SC Ideal Pixel Ideal SC Figure 15: he RMS of the local x residuals for barrel modules of the Pixel an SC detectors as a function of the iteration during the CSC exercise. SC detectors. After performing the alignment its can be seen that there is virtually no difference between the ideal and aligned distributions. Figure 15 illustrates the RMS of the local x residuals as a function of iteration. he large drop in the residual RMS between iterations and 4 is due to iteration 4 being the first iteration at Level prior to that they were Level 2 iterations. he residual bias on each layer can also be seen to converge during the alignment procedure in figure 16; 6 Validation of the Alignment he alignment algorithms that were used to derive this so-called first-pass alignment set (COOL database tag: OLFCOND-CSC--1-4), as described in Sections and 4, are based on the minimization of track residuals. While this is a necessary criterion it is not sufficient to guarantee the correct convergence of the algorithm. he presence of possible residual systematic misalignments is referred to as so-called weak modes. he InDetAlignmentMonitoring is part of the standard AHENA monitoring which is run during data reconstruction to monitor data quality. It produces a set of about 1 physics plots targeted to assess the quality of the underlying alignment set. he following categories of quantities are being monitored: hit efficiencies, generic track distributions, residual distributions, the invariant mass of resonances, like J/Ψ, Υ or Z, properties of long lived particles, electrons, muons reconstructed in the muon spectrometer, cosmics, primary and secondary vertices and the reconstructed beamline. Most of the monitoring plots are made from single tracks in MinBias data, with the exception of the 16

17 Average x residual (µm) Layer Layer 1 Layer 2 Average x residual (µm) 6 Layer Layer 1 4 Layer 2 2 Layer (a) Pixel barrel (b) SC barrel Figure 16: he average local x residual for each layer in the barrel of the (a) Pixel and (b) SC detectors Arbitrary units Ideal layout Aligned layout Arbitrary units Ideal layout Aligned layout d (mm) χ 2 /DoF Figure 17: Left: d distribution. Right:χ 2 /ndof, both for MinBias MC simulation. resonances which use the muon stream and muon triggers, and the electron plots use the electron stream and electron triggers. In the following a small set of monitoring plots is shown and discussed to illustrate the quality of the first-pass alignment set. Data reconstructed with the first-pass alignment set (aligned layout, OLFCOND- CSC--1-4) is compared with the ideal layout, using the ideal alignment (OLFCOND-CSC--1-1). he MinBias plots roughly correspond to the statistics expected in the express stream from one store at low luminosity. he plots monitoring the hit efficiencies show no deterioration as compared to the ideal layout. his means that the pattern recognition is not affected by the first-pass alignment. he track parameter distributions show slight deterioration in resolution and small biases, and the trackχ 2 /ndof is slightly affected, as shown in Fig. 17. Biases in the reconstructed trackφand z distributions can only be seen in comparison with the truth parameters, as shown in Fig 18. he CSC geometry is characterized by a very large misalignment of the outer SC barrel layer with respect to all other layers. While all other layers have residual distributions centered around zero, the outer SC layer shows features indicating the presence of residual misalignments, see Fig. 19. Fig. 2 shows the effect of residual misalignments on muon tracks, reconstructed only in the Inner Detector, from Z µµ events for an integrated luminosity of about 14 pb 1. Fitted Gaussian widths of the reconstructed Z µµ mass peaks are 2.6 GeV for a perfectly aligned detector and. GeV after the firstpass alignment. Fig. 2 also shows a charge- and p -dependent bias after the first-pass alignment, indicating 17

18 Arbitrary units Ideal layout Aligned layout Arbitrary units Ideal layout Aligned layout z (reco-truth) [mm] φ (reco-truth) Figure 18: Left: z distribution. Right: φ distribution, both for MinBias MC simulation. x residual [µm] Ideal layout Aligned layout Module φ identifier x residual [µm] Ideal layout Aligned layout Module φ identifier Figure 19: Left: x residual distribution vs. module φ identifier for the outer pixel barrel layer. Right: x residual distribution vs. module φ identifier for the outer SC barrel layer, both for MinBias MC simulation. 18

19 Arbitrary units Ideal layout Aligned layout - µ + + µ + µ - µ Ideal layout Aligned layout m µµ (GeV) p (GeV) Figure 2: Left: reconstructed Z mass from dimuon pairs from Z µµ events. Right: normalized difference of number of reconstructed negatively and positively charged muons from Z µµ events. Distributions are shown for both an ideal Inner Detector (perfectly aligned, OLFCOND-CSC--1-1) and after the underlying alignment. the presence of a weak mode. he energy of an electron can be measured very precisely in the calorimeter. he ratio of energy over momentum (E/p) of a charged particle is centered approximately at the value of one, with tails, caused by bremsstrahlung. Fig. 21 shows the E/p charge asymmetry as a function of curvature and the charge asymmetry as a function of E/p for electrons from Z ee events for an integrated luminosity of about 7 pb 1. Both plots are independent of an absolute calorimeter calibration. It is only required that E/p be independent of the particle s charge, which is given, neglecting the level of a few MeV. Both plots indicate the presence of residual systematic misalignments, confirming what is shown in Fig Summary and Outlook his note describes the production and validation of the set of alignment constants for the ALAS detector paper. For the initial CSC as-built-geometry of the ID some weak modes were incorporated on purpose, like a curl leading to a bias in the momentum measurement. he size of the introduced misalignment are probably exaggerated. However, by far not all possible deformations were introduced and deformations based on coherent movements of detector modules like a twist or the telescope effect need to be studied in more detail at a later stage. wo different track samples were simulated and applied to the alignment algorithm. A multimuon sample with ten muons per event with all tracks originating from the same vertex (about 1k events) and a cosmic ray sample (with and without B-field, about 1k tracks). First, the Si part of the detector was aligned internally using Si tracks only with several iterations. Afterwards the R was aligned with combined Si and R tracks in several iterations. he quality of the derived alignment constants was estimated using the AHENA monitoring package applied to simulated minimum bias events and events with resonance decays. he control observables indicated some residual alignment effects after the alignment, in particular in the measurement of the momentum. he reconstructed invariant mass of the Z resonance was increased from 2.6 GeV for a perfect aligned detector to. GeV using the derived set of alignment constants. he residual misalignment contributed about 2 GeV to the overall width of the Z resonance. he residual misalignment originates from lacking statistics and even more from weak modes which could 19

20 > <E/p - > - <E/p.1.5 Ideal layout Aligned layout + e + - e e + e..2.1 Ideal layout Aligned layout /p [GeV ] E/p Figure 21: Left: E/p charge asymmetry as a function of curvature for electrons from Z ee events. Right: Charge asymmetry as a function of E/p for the same events. not be removed with the above described alignment procedure applied to the available data set. In addition constraints need to be incorporated to the alignment approach in order to remove the residual misalignment to enhance the performance of the ALAS inner detector. References [1] A. Ahmad, D. Froidevaux, S. González-Sevilla, G. Gorfine and H. Sandaker. Inner Detector as-built detector description validation for CSC. 27. AL-INDE-IN [2] A. Abdesselam et al. he ALAS Experiment at the CERN Large Hadron. 28. Submitted to JINS. [] A. Abdesselam et al. Combined performance tests before installation of the ALAS Semiconductor and ransition Radiation racking Detectors. 28. Submitted to JINS. [4] [5] P. Bruckman de Renstrom, S. Haywood and A. Hicheur. Global chi2 approach to the Alignment of the ALAS Silicon racking Detectors, 25. AL-INDE-PUB [6] P. Bruckman de Renstrom and S. Haywood. PhyStat5 Proceedings, IC Press. 26. [7] A. Bocci and W. Hulsbergen. R Alignment for the SR1 Cosmics and Beyond. AL-INDE-PUB- 27-9, 27. [8] J. Alison et al. Study of the Clocking Effect in the R Alignment. Note in preparation. [9] [1] 2

21 A Inner Detector misalignments for CSC In his section the Inner Detector misalignments generated for CSC exercise are summarized. A.1 Silicon misalignments for CSC For the CSC exercise misalignments of the Silicon part of the ID at different geometry levels are generated. his misaligned geometry was used to exercise the different alignment algorithms with using realistic detector description, as close as possible to the real as-built experiment. hose misalignments were introduced in terms of Alignableransform objects, each of which contains a list of alignable transforms and associated identifiers. Each alignable transform was defined in terms of a HepransformD matrix, created from a translation and a rotation of the object to be moved. hree different level of misalignments were introduced for the Silicon: Level 1 transforms: identifier of each Silicon subsystem stored for each alignable transform. Level 2 transforms: identifier of layers/disks stored for each alignable transform. Level transforms: identifier of modules stored for each alignable transform. All misalignment numbers shown in the following silicon subsections have been extracted from [9]. A.1.1 Silicon: Level 1 transforms In the following table the numbers for the misalignments to be applied to the Pixel and SC subdetectors as level 1 are displayed. In this case, the reference frame corresponded to the global ALAS coordinate system, where x is horizontal, y vertical and z along the beamline, andα,βandγare rotations around each of the previous axis respectively. In the table 2 displacements are given in mm and rotations in mrads. he Pixel detector will be treated as a single unit, without relative misalignment between the barrel and the endcaps. Level 1 ransforms System x y z α β γ Pixel detector SC Barrel SC Endcap A SC Endcap C able 2: Silicon: Level 1 displacements A.1.2 Silicon: Level 2 transforms In the table the numbers for the misalignments to be applied for the Pixel and SC layers/disks as level 2 are shown. he coordinate system is the same as in the level 1 and the global displacements are given in mm and rotations in mrads. In the case of Pixel disks, displacements were generated as follows: from a flat distribution of width [-15,+15]µm for x and y displacements from a flat distribution of width [-2,+2]µm for z displacements from a flat distribution of width [-1,+1] mrad for the rotations defined byα,βandγangles. 21

22 Level 2 ransforms System layer x y z α β γ Pixel Barrel SC Barrel SC Endcap A SC Endcap C able : Silicon: Level 2 displacements A.1. Silicon: Level transforms In the table 4 the numbers for the misalignments to be applied for the Pixel and SC modules at level are displayed. he coordinate x is along the module measuring direction (i.e. along short-pixels for Pixel modules, across strips for SC modules), y along the perpendicular direction to x within the module plane (i.e. along long-pixels for Pixel modules, along strips for SC modules), and z is defined in the direction out-of the module plane. he three angles,α,β andγ correspond to rotations around the three local axis, respectively x, y and z. Displacements are given in mm and rotations in rads. hese misalignments were generated using a flat distributions of width defined by the numbers quoted in the table 4. Level ransforms System x y z α β γ Pixel Barrel modules Pixel Endcap modules SC Barrel modules SC Endcap modules able 4: Silicon: Level displacements 22

23 A.2 R misalignments for CSC For the R misalignments different levels were also generated. hose misalignments were, again, introduced in terms of Alignableransform objects, each of which contains a list of alignable transforms and associated identifiers as in the case of the Silicon. he R was misaligned at two levels: Level 1 (Global transform): identifier of the R(barrel/endcap A/endcap C) were stored for each alignable transform. Level 2 (Module level transform): identifier of modules stored for each alignable transform. All misalignment numbers that will be displayed in the following R subsections have been extracted from [1]. A.2.1 R: Global transform (Level 1) he whole R (barrel/endcap) was transformed with the numbers given in the table 5. he coordinate system is the same as in the level 1 and level 2 for the Silicon transforms case and the global displacements are given in mm and rotations in mrads. R Global ransforms System x y z α β γ Barrel Endcap A Endcap B able 5: R Global ransforms (so-called Level 1) A.2.2 R: Module level transform (Level 2) At this point, only barrel modules could be shifted. he final systematic and random shifts for CSC are given in the table 6. Systematic and random shifts are in R. For the random shifts, flat distributions of width defined by the numbers given in the table 6 were generated and added to the systematic shifts. he coordinate system is the same as in the previous table (5) and R shifts are given in mm. R modules level ransforms System Layer R (systematic) R (random) α β γ +1. ±.2... Barrel ± ±.... able 6: R: Level 2 ransforms (modules level) Note that there was a bug in the CSC geometry description for the R at this level, where one barrel module (layer, phi sector 26) was not misaligned. Anyhow, this had no impact on alignment results since the initial misalignment was not supposed to be known, i.e. the alignment process was blind with respect to the true misalignment. 2

24 B Error Scaling he motivation for including the rack Error Scaling in the track reconstruction is to inflate hit errors to maintain the tracking efficiency in the fit, scores, etc. his feature is used for the kick-start of the alignment, i.e when a non-aligned geometry description is used. he track hit error correction is as follows: where: a: correct calibration (added as a factor to the original hit error). c: residual misalignment (added in quadrature to the scaled hit error). σ corrected = a σ c (1) he table 7 shows the numbers applied to the IndetrkErrorScaling rel1 tag used while aligning the CSC exercise, starting from the nominal geometry. Once the alignment was done, the error scaling factors were estimated again for the new detector positions, derived from the alignment constants, and the factors were included in the COOL database within the tag OLFCOND-CSC hese numbers are shown in table 8. For tag OLFCOND-CSC--1-4 no error scaling was estimated and the nominal values are use (a=1. and c=.). Finally, even the perfect case, also called ideal alignment, had a set of error scaling numbers associated, as it is shown in table 9. Comparing table 9 with tables 7 and 8, one can see that only the c parameter was tuned as it was defined as the residual misalignment factor. he table 7 shows the numbers applied to the IndetrkErrorScaling rel1 tag used while aligning the CSC exercise. System Residual type Scale factor (a) error (c) Pixel Barrel Phi Pixel Barrel Eta Pixel Endcap Phi Pixel Endcap Eta SC Barrel Phi SC Endcap Phi R Barrel Phi R Endcap Phi MD Barrel Phi 1 MD Endcap Phi 1 RPC Barrel Phi 1 RPC Barrel Eta 1 GC Endcap Phi 1 GC Endcap Eta 1 CSC Endcap Phi 1 CSC Endcap Eta 1 able 7: Error Scaling values used for the CSC exercise (IndetrkErrorScaling rel1 tag) when a nonaligned detector description is used. 24