August 26, 2003P. Nilsson, SPD Group Meeting1 Paul Nilsson, SPD Group Meeting, August 26, 2003 Test Beam 2002 Analysis Techniques for Estimating Intrinsic Resolution An estimate of the intrinsic resolution of the SPD from 2003 Beam Tests J. Conrad & P. Nilsson

August 26, 2003P. Nilsson, SPD Group Meeting2 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

August 26, 2003P. Nilsson, SPD Group Meeting3 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

August 26, 2003P. Nilsson, SPD Group Meeting4  Preproc data decoding  (Noisy pixel removal)  Alignment  Tracking  Proc. data encoding Preprocessing and Reconstruction Raw data Converter settings.par FILE Raw_data_file[n].dat PARAMETER n... raw2root Preprocessed.root settings.par FILE Preprocessed.root... analyze Processed.root Analyser Executable Output Input control file analysis.C Executable Output Input control file ROOT macro(s)  Raw data decoding  Clustering of pixels  Event sorting  Noisy pixel removal  Preproc. data encoding CASTOR (Step 1)(Step 3) (Step 2)(Step 4) ANALYSIS DB (Step 5) www (Step 6) pre-analysis.C ROOT macro(s)

August 26, 2003P. Nilsson, SPD Group Meeting5 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)

August 26, 2003P. Nilsson, SPD Group Meeting6 “Typical” track quality    2 distributions  Residual distributions XZ-plane YZ-plane

August 26, 2003P. Nilsson, SPD Group Meeting7 Assessment of Intrinsic Resolution  General strategy:  Start from measured residual distribution Convolution of intrinsic detector resolution (flat pdf) and “tracking error” (Gauss pdf) Convolution of intrinsic detector resolution (flat pdf) and “tracking error” (Gauss pdf)  Calculate “tracking error”  Knowing tracking error  get intrinsic resolution

August 26, 2003P. Nilsson, SPD Group Meeting8 “Tracking Error”  Tracking Error : Contribution of the measurement error to the difference (x proj – x hit ) Contribution of the measurement error to the difference (x proj – x hit )  In our case: x = az +b, z = 0 in test plane, b = x proj b = x proj σ tracking = σ(b)

August 26, 2003P. Nilsson, SPD Group Meeting9 Tracking Error (2)  Tracking error will depend on σ i σ 2 i = σ 2 intrinsic + σ 2 multiple 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

August 26, 2003P. Nilsson, SPD Group Meeting10 Multiple Scattering (1) Material budget (p-run) SENSOR (Si) BUMP BONDS (Sn-Pb) CHIP (Si) Au+Cu GLUE (Epoxy) PCB (G10) Thickness (  m) X 0 (cm) x/X 0 (%) & plane 1,2,4, 150 plane 0, eff x plane 2, 200 plane 0,1,3, Beam direction TOTAL RADIATION LENGTH Al (Plane 2)

August 26, 2003P. Nilsson, SPD Group Meeting11 Assume scattering in each plane by an angle where  cp = 120GeV, z = 1, and x/X 0 = etc. Air is not included (negligible). Remember the position in the previous plane, project into the next Multiple Scattering (2)

August 26, 2003P. Nilsson, SPD Group Meeting12 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 Multiple Scattering (3)

August 26, 2003P. Nilsson, SPD Group Meeting13 The χ 2 Method (Tracking error cont.) In the XZ-projection plane:  2  track  2  track 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  2 = 1  XZ, track For a 68% confidence interval: In the YZ-projection plane:  2 = 1  YZ, track For a 68% confidence interval: XZ-plane YZ-plane

August 26, 2003P. Nilsson, SPD Group Meeting14 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 z i.  XZ, Analytical =  YZ, Analytical Because of rotated tracking planes

August 26, 2003P. Nilsson, SPD Group Meeting15 Intrinsic Resolution  Traditional approximation: σ 2 intrinsic = σ 2 residual – σ 2 tracking  “Hypothesis test” - method

August 26, 2003P. Nilsson, SPD Group Meeting16 “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” “Data compatible with simulated distribution”  Reject hypothesis if test statistics < critical value (Kolmogorov-Smirnov / χ 2 test)

August 26, 2003P. Nilsson, SPD Group Meeting17 Result: sample output of routine This file contains 6891 tracks > 6857 Using offset: e-05 Hypothesis accepted by KS Hypothesis accepted by KS Hypothesis accepted by KS Hypothesis accepted by KS Hypothesis accepted by KS Loop completed Tracking resolution Start value End value Step size Number of pseudo-events Short pixel dimension Residuals from data + toy MC

August 26, 2003P. Nilsson, SPD Group Meeting18 Results: Intrinsic resolution for different thresholds Threshold Short pixel dimension, 1 pixel cluster in test plane Error bars correspond to hypotheses that were not rejected by the tests

August 26, 2003P. Nilsson, SPD Group Meeting19 1 Pixel and 2 Pixel Clusters 1px. 2px. smaller threshold larger threshold Short pixel dimension 1,2 px clusters in test plane

August 26, 2003P. Nilsson, SPD Group Meeting20 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  use the newly found intrinsic resolution to re-estimate the tracking resolution  Iterate to get the final tracking error However…

August 26, 2003P. Nilsson, SPD Group Meeting21 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 Use intrinsic resolution at PRE_VTH 170 to get new tracking error

August 26, 2003P. Nilsson, SPD Group Meeting22 Iterative Method Initial tracking error over- estimated Tracking error iterated from short dimension only

August 26, 2003P. Nilsson, SPD Group Meeting23 Iterative Method

August 26, 2003P. Nilsson, SPD Group Meeting24 2px/1px After Iteration Using initial tracking error estimate After iterating tracking error

August 26, 2003P. Nilsson, SPD Group Meeting25 Conclusions  Results for 1 pixel and 2 pixel clusters (no tilt) at ~30 mV ( PRE_VTH 210 ): σ 1px short = ( 8.9 ± 1.0 ) µm σ 1px short = ( 8.9 ± 1.0 ) µm σ 1px long = (120.4 ± 1.7 ) µm σ 1px long = (120.4 ± 1.7 ) µm σ 2px short = ( 8.2 ± 0.9 ) µm σ 2px short = ( 8.2 ± 0.9 ) µm σ 2px long = (116.0 ± 1.7 ) µm σ 2px long = (116.0 ± 1.7 ) µm σ Track = Final tracking error: σ Track = 10.6  m