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Techniques for Estimating Intrinsic Resolution

Techniques for Estimating Intrinsic Resolution. Paul Nilsson, SPD Group Meeting , August 26, 2003. An estimate of the intrinsic resolution of the SPD from 2003 Beam Tests J. Conrad & P. Nilsson. Test Beam 2002 Analysis. Contents: Intrinsic Resolution. The 2003 test beam

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Techniques for Estimating Intrinsic Resolution

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  1. Techniques for Estimating Intrinsic Resolution Paul Nilsson, SPD Group Meeting , August 26, 2003 An estimate of the intrinsic resolution of the SPD from 2003 Beam Tests J. Conrad & P. Nilsson Test Beam 2002 Analysis P. Nilsson, SPD Group Meeting

  2. Contents: Intrinsic Resolution • The 2003 test beam • Preprocessing and tracking • Assessment of intrinsic resolution • Calculation of the “tracking error” • Measurement error and Multiple Scattering (2 different methods) • Residuals  intrinsic resolution (3 different methods) • Iterative Method P. Nilsson, SPD Group Meeting

  3. The 2003 Test Beam • Proton/pion beam at 120 GeV/c • Heavy ion beam (In) at 158 GeV/c The study presented here is based on proton beam data Setup: Two minibuses, each with two single chip assemblies, constituting four reference planes (0, 1, 3 and 4). Plane 2 is the plane under study P. Nilsson, SPD Group Meeting

  4. Preprocessing and Reconstruction Analyser Input control file Input control file settings.par FILE Raw_data_file[n].dat PARAMETER n ... settings.par FILE Preprocessed.root ... Raw data Converter (Step 1) (Step 3) Executable Executable CASTOR raw2root analyze Output Output (Step 2) (Step 4) Preprocessed.root Processed.root ROOT macro(s) ROOT macro(s) (Step 5) pre-analysis.C analysis.C • Preproc data decoding • (Noisy pixel removal) • Alignment • Tracking • Proc. data encoding • Raw data decoding • Clustering of pixels • Event sorting • Noisy pixel removal • Preproc. data encoding ANALYSIS DB (Step 6) P. Nilsson, SPD Group Meeting www

  5. Data Cleaning • Used dataset: c0r0_tilt0_thXXX • Several noisy pixels were removed • Only events with 1 hit per reference plane were accepted (i.e. 4 reference points for the track candidate) (Trivial alignment due to focused beam data) P. Nilsson, SPD Group Meeting

  6. “Typical” track quality YZ-plane XZ-plane • 2 distributions • Residual distributions P. Nilsson, SPD Group Meeting

  7. Assessmentof Intrinsic Resolution • General strategy: • Start from measured residual distribution Convolution of intrinsic detector resolution (flat pdf) and “tracking error” (Gauss pdf) • Calculate “tracking error” • Knowing tracking error  get intrinsic resolution P. Nilsson, SPD Group Meeting

  8. “Tracking Error” • Tracking Error : Contribution of the measurement error to the difference (xproj – xhit) • In our case: x = az +b, z = 0 in test plane, b = xproj σtracking = σ(b) P. Nilsson, SPD Group Meeting

  9. Tracking Error (2) • Tracking error will depend on σi σ2i= σ2intrinsic + σ2multiple scattering Error on the cluster coordinates in the tracking planes Initially assume to be width /  Select events with 1 pixel clusters in tracking planes Has to be calculated P. Nilsson, SPD Group Meeting

  10. Multiple Scattering (1) Thickness (m) X0(cm) x/X0(%) Material budget (p-run) PCB (G10) 1000 19.4 0.5155 75 44.37 0.0169 GLUE (Epoxy) 1 + 35 0.33 & 1.43 0.2751 Au+Cu 725plane 1,2,4,150plane 0,3 9.36 0.7746 CHIP (Si) BUMP BONDS (Sn-Pb) 0.385eff 0.95 8.8x10-4 SENSOR (Si) 300plane 2 , 200plane 0,1,3,4 9.36 0.3205 10 8.9 0.0112 Al TOTAL RADIATION LENGTH (Plane 2) Beam direction P. Nilsson, SPD Group Meeting

  11. Multiple Scattering (2) Assume scattering in each plane by an angle where cp = 120GeV, z = 1, and x/X0 = 0.0192 etc. Air is not included (negligible). Remember the position in the previous plane, project into the next P. Nilsson, SPD Group Meeting

  12. Multiple Scattering (3) Results: The MS contributions, i.e. the square of widths of the MS gaussians (the position distributions) are then added to the position errors of the cluster positions P. Nilsson, SPD Group Meeting

  13. The χ2 Method (Tracking error cont.) • Idea: use 2 information to calculate the track resolution by varying the track fit constant (x,y = f(z) = az + b, vary b and redo the 2 calculation) • The track resolution can be read out from the resulting parabolas XZ-plane In the XZ-projection plane: For a 68% confidence interval: 2 = 1XZ, track track 2 YZ-plane In the YZ-projection plane: For a 68% confidence interval: 2 = 1YZ, track track 2 P. Nilsson, SPD Group Meeting

  14. Analytic Calculation (Tracking error cont.) For a linear fit the errors in the fit parameters can be calculated using standard error propagation. They are found to be where i is the error in the variable zi. XZ, Analytical = YZ, Analytical Because of rotated tracking planes P. Nilsson, SPD Group Meeting

  15. Intrinsic Resolution • Traditional approximation: σ2intrinsic = σ2 residual – σ2tracking • “Hypothesis test” - method P. Nilsson, SPD Group Meeting

  16. “Hypothesis Test” Method • Toy MC to convolute: • Gauss (estimated tracking error) • Flat (intrinsic resolution = ) • Loop over parameter w and test hypothesis: “Data compatible with simulated distribution”  Reject hypothesis if test statistics < critical value (Kolmogorov-Smirnov / χ2 test) P. Nilsson, SPD Group Meeting

  17. Result: sample output of routine This file contains 6891 tracks << Processing tracks... >> 6857 Using offset: -9.036e-05 Hypothesis accepted by KS 20 0.015 Hypothesis accepted by KS 21 0.0155 Hypothesis accepted by KS 22 0.016 Hypothesis accepted by KS 23 0.0165 Hypothesis accepted by KS 24 0.017 Loop completed Tracking resolution 0.01117 Start value 0.005 End value 0.0175 Step size 0.0005 Number of pseudo-events 100000 Short pixel dimension P. Nilsson, SPD Group Meeting Residuals from data + toy MC

  18. Results: Intrinsic resolution for different thresholds Short pixel dimension, 1 pixel cluster in test plane Error bars correspond to hypotheses that were not rejected by the tests Threshold P. Nilsson, SPD Group Meeting

  19. 1 Pixel and 2 Pixel Clusters Short pixel dimension 1,2 px clusters in test plane smaller threshold 1px . 2px . larger threshold P. Nilsson, SPD Group Meeting

  20. Iterative Method • Tracking error estimate relies on knowledge of 1 pixel intrinsic resolution at a given threshold  use the newly found intrinsic resolution to re-estimate the tracking resolution • Iterate to get the final tracking error However… P. Nilsson, SPD Group Meeting

  21. Use intrinsic resolution at PRE_VTH 170 to get new tracking error Iterative Method • Tracking planes were run at PRE_VTH 200 and were not identical to test plane (300 m sensor vs 200 m) • Try to find conditions when intrinsic resolution of test plane is comparable to tracking planes • Probability to obtain 1 or 2 px clusters is proportional to size of sensitive region Use ratio between 1 and 2 px clusters to find threshold where test plane has similar resolution as tracking planes Deviation from 1 of number of 1 to 2 px clusters in test plane to the tracking planes as a function of PRE_VTH P. Nilsson, SPD Group Meeting

  22. Iterative Method Tracking error iterated from short dimension only Initial tracking error over-estimated P. Nilsson, SPD Group Meeting

  23. Iterative Method P. Nilsson, SPD Group Meeting

  24. 2px/1px After Iteration After iterating tracking error Using initial tracking error estimate P. Nilsson, SPD Group Meeting

  25. Conclusions • Results for 1 pixel and 2 pixel clusters (no tilt) at ~30 mV (PRE_VTH 210): σ1pxshort= ( 8.9 ± 1.0 ) µm σ1pxlong = (120.4 ± 1.7 ) µm σ2pxshort= ( 8.2 ± 0.9 ) µm σ2pxlong = (116.0 ± 1.7 ) µm Final tracking error: σTrack= 10.6 m P. Nilsson, SPD Group Meeting

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