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

2. 2 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 m m) 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 Pixel clusters have a characteristic shape caused by Lorentz drift Two-Track Separation in Pixel System

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

4. 4 Pixelav transport simulation + E-field modeling w/ TCAD 9.0 - data well described by tunable double-junction model from F =(0.5-6)x10 14 n eq /cm 2 Use to calculate a priori cluster shapes for improved analysis technique 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,

5. 5 Sum charges on all pixels: Q clus Truncate individual pixel signals to cot b -dependent maximum - sum projections: P y/x i 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 P y i and P x i : -> scale and translate shape to fit Fit projected cluster shapes to simulated shapes (templates): Template-based Reconstruction Algorithm

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

7. 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. 8 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 Q clus x( f ) resolution worsens at large h ? - caused by low Q clus “junk” from showering in our not-so-thin detector - ~ 7% of high- h tracks have low-Q clus hits on them Implementation in CMS Tracking

9. Pulls are sensitive to resolution tails ➡ template reconstruction kills tails! Biggest improvements are in d 0, f 0 pulls in the regions > 3 s ➡ expect to see significant S/N improvements in b/ t -tagging d0d0 + template alg + standard alg f0f0 Effect of 2nd pass on track parameters 10 GeV m ’s

10. 10 Goodness-of-fit A by-product of the template fitting procedure is a x 2 that reflects the consistency between the shapes of the cluster projection and the interpolated template  template object stores the expected x 2 distribution in a simple parameterization that depends upon Q clus - 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 No Probability Cut P>10 -3

11. 11 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) Track Seeding y (global z) x (global f)

12. 12 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 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: Seed Generator 0.13 s/event Seed Cleaner 0.06 s/event Kalman Filter 1.80 s/event 1085k seeds 476k seeds 37.6k tracks 1.92 s/event 37.0k tracks 1.15 s/event Kalman Filter 0.96 s/event

13. 13 Use 80-120 GeV P T QCD events Track counting doesn’t need re- calibration - track probability also improves /wo calib Improvement in S/N is in range 2-3! 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 Template Reco Only Template Seeding+Reco b-efficiency udsg-efficiency

14. 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. 15 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 Step 1:  first pass tracking with “loose” cuts on x 2 ✴ road search and/or ✴ CTF with simple seeder ✴ templates in second pass only hit 2hit 1

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