Pixel Cluster Splitting Using Templates

1. Pixel Cluster Splitting Using Templates D. Fehling, G. Giurgiu, P. Maksimovic, S. Rappoccio, M.Swartz Dept of Physics+Astronomy, Johns Hopkins University

2. Two-Track Separation in Pixel System Pixel clusters have a characteristic shape caused by Lorentz drift • clustering algorithm needs to include corner adjacency • thresholds can create apparently unlikely cluster shapes • minimum two-track separation in f (local x) is ~3 pixels (300 mm) • minimum two-track separation in z (local y) varies from ~2 pixels (h=0) to ~12 pixels (h=2.5) or 0.3-18 mm • standard and template reconstruction will fail when clusters merge • template reco will return bad probabilities when this happens

3. Template Reconstruction Slides 4-13 summarize the pixel template reconstruction technique. Lots more detail can be found in CMS Note-2007/033

4. Sensor Modeling Over the last 4 years, we (VC + MS) have successfully modeled irradiated pixel sensors fabricated on DOFZ substrates at several F and T, • Pixelav transport simulation + E-field modeling w/ TCAD 9.0 • data well described by tunable double-junction model from F =(0.5-6)x1014 neq/cm2 • Use to calculate a priori cluster shapes for improved analysis technique

5. Template-based Reconstruction Algorithm Fit projected cluster shapes to simulated shapes (templates): • Sum charges on all pixels: Qclus • Truncate individual pixel signals to cotb-dependent maximum • sum projections: Py/xi • Account for thresholds: • add information back by creating Pseudo-Pixels at the ends of the cluster • have 50% of threshold height and 100% uncertainties • pulls fit near cluster edges and improves resolution Apply fitting procedure to projections Pyi and Pxi: -> scale and translate shape to fit

6. Comparison with Standard Algorithm After small corrections for residual effects • RMS residuals not Gaussian fit sigma (tails included) • Before irradiation, template algorithm improves the resolution at all h • for Q/Qavg<1 (~70% of all hits), 10-20% improvement • for 1<Q/Qavg<1.5 (~30% of all hits), 20-100% improvement high-h deltas

7. After irradiation, Standard technique is more affected than templates • z-resolution in both charge bands, 100% improvement • f-resolution at large h, 30-200% improvement high-h deltas

8. Implementation in CMS Tracking • Template reconstruction has moderate sensitivity to track angles • use Standard technique for first pass track finding/fitting • use Template technique in second pass track fit (angles from 1st pass) • Study with sample of simulated muon tracks • Template technique exceeds the Standard technique at all h and Qclus • x(f) resolution worsens at large h ? • caused by low Qclus “junk” from showering in our not-so-thin detector • ~ 7% of high-h tracks have low-Qclus hits on them

9. Effect of 2nd pass on track parameters • Pulls are sensitive to resolution tails • template reconstruction kills tails! • Biggest improvements are in d0, f0 pulls in the regions > 3 s • expect to see significant S/N improvements inb/t-tagging 10 GeV m’s + standard alg d0 + template alg f0

10. Goodness-of-fit No Probability Cut • A by-product of the template fitting procedure is a x2that reflects the consistency between the shapes of the cluster projection and the interpolated template • template object stores the expected x2 distribution in a simple parameterization that depends upon Qclus • convert these into x- and y-probabilities • Suppresses low-Q junk clusters that arise from secondary interactions with 1-2 % inefficiencies • Can remove low-Q with no inefficiency P>10-3

11. Track Seeding • A. Dominguez has been developing an improved pixel track seeder that compares the lengths of y-clusters (global z) in the pixel barrels • can significantly reduce the number of trial seeds and therefore the track finding time (dominates reco time) • Intrinsic y-length resolution of the templates is about twice that of the simple cluster length method • seeds have local angles, can use templates in 2nd pass • template probabilities determine consistency with angle hypotheses and are normalized to resolution • can do both x- and y-projections • can do barrel/FPix seeds • Avoids “junk” hits on tracks (may be more junk in real LHC environment) y (global z) x (global f)

12. First Seeding Results (preliminary) D. Fehling, P. Maksimovic (JHU) have created a template-based seed cleaner that works with pixel-doublet seeds. The first test was done with a sample of 750 simulated t-tbar events: 1085k seeds Kalman Filter 1.80 s/event Seed Generator 0.13 s/event 37.6k tracks 1.92 s/event 1085k seeds 476k seeds Seed Cleaner 0.06 s/event Kalman Filter 0.96 s/event 37.0k tracks 1.15 s/event • Reduces number of seeds and tracking time by factor of ~2 • Loses 1.6% of tracks • quality of lost tracks is unknown as yet • No attempt to optimize cuts or use low-Q cut yet • New seeding in CMSSW 2_0: improvement smaller but still significant

13. b-Tagging (preliminary) D. Fehling has studied the effect of the 2nd-pass template reco and templated-based seed cleaning+2nd-pass reco on b-tagging: Standard Reco • Use 80-120 GeV PT QCD events • Track counting doesn’t need re-calibration • track probability also improves /wo calib • Improvement in S/N is in range 2-3! Template Reco Only Template Seeding+Reco udsg-efficiency b-efficiency

14. Templates in Cluster Splitting • Template technique has only modest sensitivity to the track angles • 1-2 mm shifts in cluster position do not affect resolution • Template probabilities flag unlikely cluster shapes/sizes • should avoid using the probabilities at the seeding level • want to include “bad” hits on tracks (to associate merged clusters to tracks and get angle estimates) • Current version of Template Technique works in two 1-D projections • full 2-D templates are possible but don’t exist currently • very cpu intensive to generate • would be significantly slower (not usable for everyday seeding) • no resolution advantage • would improve discrimination of template probability • would improve cluster splitting capabilities • The following is a sketch of a high pt jet re-tracking algorithm based on current 1-D cluster technology

15. Step 1: • first pass tracking with “loose” cuts on x2 • road search and/or • CTF with simple seeder • templates in second pass only • Step 2: • examine template probabilities of tracked pixel hits • if small, try fitting two hit hypotheses in both projections • take the angles to be the same for both hits • should improve template probabilities • produces 4 new hits w/ 2-fold ambiguity (2-x X 2-y coords) • Step 3: • re-track event w/ tighter cuts hit 1 hit 2

16. How to Begin • Coding of a cluster splitter should be fairly straightfoward: • 1-3 weeks for initial development/coding (tuning/iterating could take longer) • initial testing with merged pixelav hits • test code needs to be developed also • 2-hit hypothesis probability needs calibration • add more info to the basic template infrastructure? • Need full re-tracking procedure • Testing splitting as part of a re-tracking procedure • need samples of problematic events • need diagnostics that identify the inefficiency and resolutions