1. Vertex and Track Reconstruction in CMS W. Adam Institute of High Energy Physics, Austrian Academy of Sciences, Vienna CMS Collaboration Perugia, Italy

2. WA, Vertex and Track Reco in CMS - Vertex062 Overview The challenges The detector Track reconstruction Baseline: track finding and fitting Advanced algorithms Special applications Vertex reconstruction Vertex fitting Primary & secondary vertex finding Conclusions & Outlook

3. WA, Vertex and Track Reco in CMS - Vertex063 The challenges pp-collisions at design luminosity (10 34 cm -2 s -2, 14TeV) 40 MHz crossing rate O(20) superimposed pileup events / crossing O(2000) charged tracks / crossing Charged track density 2.5 / cm 2 / 25ns at r = 4cm 0.15 / cm 2 / 25ns at r = 10cm 0.01 / cm 2 / 25ns at r = 110cm Trigger Level 1 »Design rate 100kHz, no tracker Levels 2-3: HLT »Reduction to 100Hz Includes (partial) track reconstruction

4. WA, Vertex and Track Reco in CMS - Vertex064 The challenges Physics requirements Highly efficient track reconstruction & low ghost rate Excellent momentum resolution »Mass reconstruction »Energy flow »Charge separation Excellent impact parameter resolution »Primary vertex reconstruction & separation of pileup »Secondary vertex reconstruction »Heavy flavour tagging Combined reconstruction »Link to ECAL and muon system

5. WA, Vertex and Track Reco in CMS - Vertex065 R=1.2m L=5.4 m The detector Full-Silicon solution for the inner tracking Excellent hit resolution, high granularity: »Good two-track separation »Low occupancy > 220 m 2 of silicon sensors Classical layout cylindrical barrel planar end cap disks Pixel

6. WA, Vertex and Track Reco in CMS - Vertex066 The detector Pixel detector close to interaction region Barrel 3 layers 768 modules R = 4.4 / 7.3 / 10.2 cm Pixel size 100  m x 150  m 48 M pixels Lorentz angle 23  Endcaps 2 x 2 layers 672 modules |z| = 34.5 / 46.5 cm Pixel size 100  m x 150  m 18 M pixels Tilted for Lorentz angle

7. WA, Vertex and Track Reco in CMS - Vertex067 R=1.2m L=5.4 m The detector Strip detectors enclosing the pixel part 4 TIB layers 6 TOB layers 2 x 9 endcap disks 2 x 3 inner disks Outer Barrel –TOB- Inner Barrel –TIB- End cap –TEC- Inner Disks –TID-

8. WA, Vertex and Track Reco in CMS - Vertex068  Z (mm) R (mm) The detector Inner Barrel 4 layers (2 stereo) Rectangular sensors (d=320  m) Pitch 80  m & 120  m Outer Barrel 6 layers (2 stereo) Rectangular sensors (d=500  m) Pitch 122  m & 183  m Inner & Endcap Disks 2 x (3+9) disks Up to 7 rings (3 stereo) Trapezoidal sensors (d = 320  m & 500  m) Mean pitch ~95  m to ~185  m

9. WA, Vertex and Track Reco in CMS - Vertex069 Track reconstruction Seeds Track Candidates Tracks Selection of first hits & initial parameters Selection of full set of hits & ambiguity resolution Parameter estimation, track quality, cleaning Pattern Recognition Track Fit

10. WA, Vertex and Track Reco in CMS - Vertex0610 Baseline track reconstruction Seeding from pixel hit pairs Why pixels? Lowest occupancy & 2dim hits! Start with one reference hit, add inner layer »Compatible with vertex region, first hit and p T limit Full algorithmic efficiency Fast ~ 30ms @ 2.8GHz for global reconstruction For commissioning and extended acceptance “mixed” and “pixelless” seeding Applies same algorithm to (inner) strip layers

11. WA, Vertex and Track Reco in CMS - Vertex0611 Baseline track reconstruction Track Finding: combinatorial Kalman Filter approach Starts with initial estimate provided by seed Fast navigation and selection of compatible sensors & hits KF for iterative growing of candidates and quality measure »Adds compatible hits (+ “null” hypothesis == hit inefficiency) b-jets, L=2x10 33 p T =120-170GeV R  uncertainty at TIB1 Px TIBTOB

12. WA, Vertex and Track Reco in CMS - Vertex0612 Baseline track reconstruction Control of combinatorial growth while iterating »Limit #candidates (ranking) »Quality filter (rejection of poor candidates) »Resolve ambiguities during and after candidate building Sufficiently fast & flexible even for dense environments! »An alternative P.R. algorithm using a road search is also available #candidates formed on TIB1 (“worst case”) with spurious hits Fraction with spurious hits Before final cleaning! B-Pix Barrel Strips (candidates with hits in all layers)

13. WA, Vertex and Track Reco in CMS - Vertex0613 Baseline track reconstruction Efficiencies Algorithmic: close to 100% except for low-E  ’s (elastic interactions) Global: for pions dominated by hadronic interactions ~ no degradation in b-jets; fake rates <0.3% (1%) in barrel (forward) muons pions ~0.35X 0 / ~0.1 0 ~1.4X 0 / ~0.6 0 Global efficiencies (  8 hits)  (  ) can be improved by requiring less hits Single particles

14. WA, Vertex and Track Reco in CMS - Vertex0614 Baseline track reconstruction Track fitting LS-fit implemented as a Kalman filter Inside-out “forward” fit »Removes approximation of building stage »optimal estimate at exit from tracker Outside-in “smoother” optimal estimate at vertex »In combination with forward fit:  optimal estimates at each layer Goodness-of-fit »Global track  2 »Compatibility of each hit Execution time is small compared to pattern recognition p T =1GeV p T ≥10GeV

15. WA, Vertex and Track Reco in CMS - Vertex0615 Baseline track reconstruction Resolution & track quality p T (rel.) Reduced  2 Transv. IP Long.. IP , p T =1GeV , p T =10GeV , p T =100GeV

16. WA, Vertex and Track Reco in CMS - Vertex0616 Advanced tracking algorithms Gaussian Sum Filter “minimal” extension of KF for non-Gaussian components: modeled by sum of Gaussians Resembles several KFs in || - measurements change parameters and relative weights Implemented in CMS SW: radiative energy loss of electrons p out /p in layers q/p true value Gaussian sum radiation Single track example

17. WA, Vertex and Track Reco in CMS - Vertex0617 Advanced tracking algorithms GSF provides an estimated pdf  more than just mean & sigma! CPU-intensive  use on pre-selected tracks Other advanced algorithms implemented in CMS Deterministic annealing filter »Adaptive tracking with high density of background hits Multi-track fitter »Simultaneous fit of narrow bundles of tracks with ambiguity resolution Electrons p T =10GeV In- / outside estimates provide measure of radiated energy KF electron fit vs. GSF GSF mode vs. mean

18. WA, Vertex and Track Reco in CMS - Vertex0618 Tracking for Pb-Pb-collisions Standard algorithms can cope with 3000 N ch /y ! Small modification to reduce CPU-time and tighter quality cuts for lower fake rate: »Start with pixel triplets instead of pairs »Don’t pre-combine hits in stereo layers »Recognize merged clusters B-Pix Barrel Strips High occupancy in first strip layers! Low fake-rate tuning Alternative working point:  ~ 90% for fake rates up to ~ 20% central Pb-Pb collisions, Nch/y = 3000-3500 efficiency fake rate

19. WA, Vertex and Track Reco in CMS - Vertex0619 HLT tracking Adapting existing algorithms Regional tracking »Reconstruct only in an externally defined region (e.g. from lower-level trigger object) Conditional tracking »Stop when required precision is achieved (e.g. to confirm p<p min ) - typically 5 layers are sufficient Use more constraints »E.g. (first estimate) of primary vertex Use alternative reconstruction Extend pixel seed pairs to triplets Fast estimation of track parameter from triplets Can be used for fast primary vertex reconstruction p T vs #hits d 0 vs #hits Full reconstruction p T resolution (GeV) d 0 resolution (  m) Barrel 2.5<p T <5 2 pixel hits 3 pixel hits 2&3 pixel hits

20. WA, Vertex and Track Reco in CMS - Vertex0620 Vertex reconstruction Vertex finding & track association Vertex fitting Primary vertex Kalman filter Secondary & tertiary vertices Robustified KFAdaptive Filters …

21. WA, Vertex and Track Reco in CMS - Vertex0621 Vertex fitting Algorithmic base: Kalman filter Tracks are iteratively added to a vertex Last track  best vertex estimate Possibility to smooth & update track parameters Complication Track  vertex association Non-Gaussian track residuals  P(  2 ) peaked at 0 Conventional robustification: “trimmed Kalman vertex fitter” Define  2 -cut / track Remove “worst” outlier and reiterate  hard assignment Simple concept, but low break-down point »Fails for highly contaminated vertex candidates CMS studies: min. compatibility = 5%

22. WA, Vertex and Track Reco in CMS - Vertex0622 Vertex fitting Adaptive fitting Iterative fit with reweighting »Introduces fractional weight / track and weight function »Starts at high T to avoid local minima »Decreases T after each iteration (“annealing”) Results in soft assignment (unless T  0) »#tracks  effective #tracks =  w i  2  pseudo-  2 »High break-down point CMS studies:  2 cut =9, geometric annealing

23. WA, Vertex and Track Reco in CMS - Vertex0623 Vertex fitting KFAdaptiveTrimmed Residuals (z) Pulls (z) ttH, m H =120GeV L=2x10 33 cm -2 s -1

24. WA, Vertex and Track Reco in CMS - Vertex0624 Vertex fitting Adaptive vertex fit »Slightly better resolution »Slower for low N track »Faster for high complexity KFAdaptiveTrimmed Rejected tracks Time / fit ttH, m H =120GeV L=2x10 33 cm -2 s -1

25. WA, Vertex and Track Reco in CMS - Vertex0625 residuals Vertex fitting Gaussian Sum Filter: accepts tracks with multi-Gaussian states »electrons from GSF track fit or parameterization of tails observed in reconstruction »Here: simple model 4 tracks 90%  (d 0 )=100  m 10%  (d 0 )=1000  m Many KF vertices with P(  2 )<0.01 GSF residuals almost without tails KF GSF P(  2 )

26. WA, Vertex and Track Reco in CMS - Vertex0626 Vertex finding Primary vertex finding Using fully reconstructed tracks Preselection (i.p. significance & p T ) & clusterization in z Robustified vertex fit & cleaning (  2 -cut and compatibility with beam line) Sorting by  p T 2 Alternative: use pixel triplets (HLT) Efficiency for finding signal PV  % Resolution (  m)  (x)  (z) Pixel triplets Resolution (  m) H  b-jets ttH b-jetsttH H  ZZ  4e H  DY, 2 

27. WA, Vertex and Track Reco in CMS - Vertex0627 Vertex finding Secondary vertex finding “Trimmed Kalman Vertex Finder” »First fit with complete set »Continue with rejected tracks “Tertiary Vertex Finder” »Start with TKVF »Choose additional tracks close to flight path »Only used for kinematics (not for position) Track  vertex assoc. efficiency purity  (%) Vertex finding efficiency purity  (%) Resolution (68% cov.) bc Flight distance 765  m550  m Angle (3D)15.5 mrad8.0 mrad

28. WA, Vertex and Track Reco in CMS - Vertex0628 Vertex finding Secondary vertex quality b-vertices c-vertices Flight distance 3D anlge Combined secondary vertex tag on 50-80GeV QCD sample c gu,d,s

29. WA, Vertex and Track Reco in CMS - Vertex0629 First Step Beyond MC Real tracks in Tracker integration tests and CMS cosmic challenge TID TEC

30. WA, Vertex and Track Reco in CMS - Vertex0630 Conclusions & Outlook A powerful set of track and vertex reconstruction algorithms Performance and application have been demonstrated in CMS Physics TDR Vol I & II New data model and software framework Basic algorithms have been ported Need to finish with advanced algorithms and validate! Commissioning and startup Becomes highest priority! Concentrate on geometry for commissioning Work on calibration issues »Alignment, material, detector condition, … We are eagerly waiting for the first tracks & vertices from the underground of LHC Point 5 !!!