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Pixel Cluster Splitting Using Templates

D. Fehling, G. Giurgiu, P. Maksimovic, S. Rappoccio, M.Swartz

Dept of Physics+Astronomy, Johns Hopkins University

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• 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

Pixel clusters have a characteristic shape caused by Lorentz drift

Two-Track Separation in Pixel System

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

Template Reconstruction

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• 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

Sensor ModelingOver the last 4 years, we (VC + MS) have successfully modeled irradiated pixel sensors fabricated on DOFZ substrates at several F and T,

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•Sum charges on all pixels: Qclus

•Truncate individual pixel signals to cotb-dependent maximum- sum projections: Py/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 Pyi and Px

i: -> scale and translate shape to fit

Fit projected cluster shapes to simulated shapes (templates):

Template-based Reconstruction Algorithm

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• 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

Comparison with Standard AlgorithmAfter small corrections for residual effects

high-h deltas

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•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

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• 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

Implementation in CMS Tracking

•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 in b/t-tagging

d0 + template alg+ standard alg

f0

Effect of 2nd pass on track parameters

10 GeV m’s

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Goodness-of-fit•A by-product of the

template fitting procedure is a x2 that 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

No Probability Cut

P>10-3

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•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 Seedingy (global z)

x (global f)

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•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 Generator0.13 s/event

Seed Cleaner

0.06 s/event

Kalman Filter1.80

s/event

1085k seeds

1085k seeds

476k seeds

37.6k tracks1.92 s/event

37.0k tracks1.15 s/event

Kalman Filter0.96

s/event

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•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!

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 RecoTemplate Reco Only

Template Seeding+Reco

b-efficiency

ud

sg-e

ffici

ency

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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

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•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 x2

✴ 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:- 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