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

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

4 Pixelav transport simulation + E-field modeling w/ TCAD 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 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 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), % improvement Comparison with Standard Algorithm After small corrections for residual effects 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, % improvement high- h deltas

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

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 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 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 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 Use 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 Templates in Cluster Splitting Template technique has only modest sensitivity to the track angles 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 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

How to Begin Coding of a cluster splitter should be fairly straightfoward: 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