1. CMS tracker reconstruction performance
University and INFN, Bari
Nicola De Filippis
9th Topical Seminar Innovative Particle and Radiation Detectors
Siena May 23-26, 2004
on behalf of
CMS collaboration
Siena May 23-26
N. De Filippis,
University and INFN Bari

2. University and INFN Bari
Outline
CMS Tracker detectors overview
Track reconstruction principles and performances
Vertex reconstruction principles and performances
Tracking for high level trigger
Performances of reconstruction in BS -+
Siena May 23-26
N. De Filippis,
University and INFN Bari

3. University and INFN Bari
The CMS detector
Siena May 23-26
N. De Filippis,
University and INFN Bari

4. Silicon pixel detector
The pixel detector consists of:
three cylindrical barrel layers at
4.4 cm, 7.5 cm and 10.2 cm
two pairs of end-cap disks at
|z| = 34.5 cm and 46.5 cm up to |h| < 2.2.
pixel size: 100 x 150 mm2
hit resolution is ~10 m in the r-f plane
17 m in r-z plane
Occupancy is ~ 10-4
Siena May 23-26
N. De Filippis,
University and INFN Bari

5. Silicon strip detector
The SST covers the radial region between 20 and 110 cm
6 TOB
Thickness ~ 500mm
pitch ~ 180 mm
4 TIB
9 TEC
Thickness ~ 320mm
pitch ~ 122 mm
3TID
The layers 1-2 TIB and TOB, the first two rings of TID and rings 1, 2 and 5 of TEC are instrumented with 2 sets of single-side detectors glued back-to-back with a stereo angle of 100 mrad.
Silicon strip : r-f = m, sz = 500 mm
Siena May 23-26
N. De Filippis,
University and INFN Bari

6. Requirements for the CMS tracker
Efficient & robust Pattern Recognition algorithm
Fine granularity to resolve nearby tracks
Fast response time to resolve bunch crossings
Ability to reconstruct narrow heavy object
1~2% pt resolution at ~ 100 GeV
Ability to operate in a crowded environment
Nch/(cm2*25ns) = at 10 cm from PV
Ability to tag b/t through secondary vertex
Good impact parameter resolution
Reconstruction efficiency
95% for hadronic isolated high pt tracks
90% for high pt tracks inside jets
Ability to operate in a very high radiation environment
Silicon detectors will operate at -7°C  -10°C to contain reverse
annealing and limit leakage current
due to
high track multiplicity
300 MeV/c < pT up to many hundred GeV/c
secondary interactions
multiple scattering
Siena May 23-26
N. De Filippis,
University and INFN Bari

7. Principles of track reconstruction
Track reconstruction is based on:
the track model which describes the trajectory of a particle  equations of motion of a charged particle in a magnetic field
“process noise”: stochastic processes added to take into account the matter
Description of tracker material in a simplified way  speed up the reconstr.
all material is assumed to be concentrated on thin surfaces
the material properties of each detector layer described by two numbers:
the thickness in units of radiation length
the thickness multiplied by the mean ratio of atomic number to atomic mass
Two kinds of effects taken into account:
energy loss (for electrons due to Bremsstrahlung, for all other particles due to ionization with Bethe-Block formula)
multiple scattering (using gaussian approximation)
Siena May 23-26
N. De Filippis,
University and INFN Bari

8. Track reconstruction steps
seed generation: it provides initial trajectory candidates
internal to the tracking detector (inner tracker or muon system)
external by using input from other detectors (calorimeters).
building trajectories starting from seeds: it is based on the Kalman filter formalism and consists of:
layer navigation provides a list of reachable layers from the current layer in a given direction.
propagator: each reachable layes provides measurements (rec hits) compatible with a trajectory candidate
updator: each compatible measurement is combined with the corresponding predicted trajectory state
trajectory cleaning by resolving of ambiguities among multiply reconstructed trajectories.
smoothing of a trajectory: it is the procedure of combining the forward and backward fits; the “backward fit” is performed starting from outside, gives optimal knowledge of the parameters at origin.
Siena May 23-26
N. De Filippis,
University and INFN Bari

9. University and INFN Bari
Track fitting methods
• Track fits with hard assignment of hits to tracks, where a hit either does or does not contribute to a track:
The Global Fit: based on the Least Squares Method (LSM)
The Kalman Filter: based on a recursive LSM fit, used for estimating the states of a stochastic model evolving in time (a dynamic system) It has good performance, high efficiency and a low fake rate.
The Gaussian Sum Filter: relevant for the reconstruction of electrons which suffer from large energy losses due to bremsstrahlung whose distribution is highly non Gaussian
• Track fits with soft hit assignment, where hits contribute to a track according to their assigned weights (associated assignment probability) :
The Elastic Arm Algorithm: works with deformable track templates which are “attracted” to the hits
The Deterministic Annealing Filter: replaces competition between tracks by competition between hits
The Kalman Filter and the Deterministic Annealing Filter are implemented in CMS reconstruction program (ORCA)
Siena May 23-26
N. De Filippis,
University and INFN Bari

10. Tracking performances
A track is reconstructed if:
more than 50% of the hits are shared with a simulated track
at least 8 hits in the tracker of which at least 2 are in the pixel detector.
The “algorithmic efficiency”  the efficiency of the trajectory builder
The “global efficiency”: it includes the acceptance, hit efficiency and any other factor affecting reconstruction, in addition to the efficiency of the algorithm.
Single muons events
Single pions events
At |η|=2.4 inefficiency caused by the lack of coverage of the end-cap disks.
Degradation
due tracker material
Siena May 23-26
N. De Filippis,
University and INFN Bari

11. Material budget of CMS tracker
Radiation lengths of tracker:
Interaction lenght of tracker:
A lot of material!
….killing tracks
Siena May 23-26
N. De Filippis,
University and INFN Bari

12. Tracker performances: s(pT) and s(d0)
The pT resolution is better than 2% for pT < 100 GeV/c up to |η|=1.75; at large η the resolution degrades due to the reduction of the lever arm.
At high momentum, the transverse impact parameter d0 resolution is constant and is dominated by the hit resolution of the first hit in the pixel detector.
At lower momenta multiple scattering becomes significant and the h dependence reflects the amount of material traversed by tracks
pT resolution
d0 resolution
(d0) = f(pT,) pT = 1 GeV/c: 0.1  0.2 mm
high pT: 10  20 m
gap between the barrel and the end-cap disks
Siena May 23-26
N. De Filippis,
University and INFN Bari

13. Vertex reconstruction
Why vertex reconstruction?
to reconstruct primary and secondary vertexes
Vertex reconstruction consists of:
Vertex finding (pattern recognition problem)
given a set of tracks, separate it into clusters of compatible tracks
inclusively: not related to a particular decay channel
search for secondary vertices in a jet
exclusively: find best match with a decay channel
simple topologies (H  4) or B-physics channels
generally requires generation of combinations, selection of topologies and kinematic constraints
Vertex fitting (estimation problem )
find the 3D point most compatible with a set of tracks, grouped together at vertex finding stage
Siena May 23-26
N. De Filippis,
University and INFN Bari

14. Primary vertex findingz
10-30
4cm
7cm z0
Pixel hit pairing in R-z and R-
d01 mm , PT  1 GeV
Matching with 3rd layer  track candidate
PV candidate if  3 track cross z-axis
PV list  Signal vertex from PT and Ntracks
Cleaning of tracks not pointing to PV
Track straight line approximation in z
The efficiency of the PV algo is high
In the HLT event samples the signal PV is always found with an efficiency of better than 95%.
Primary vertex resolution
Average GHz
(High Lumi)
Pixel detectors  fast reconstruction of the PV with resolution ranging from 20 to 70 m  improved also using the microstrip tracker information with resolution of about 15 mm but at the expense of CPU time
Siena May 23-26
N. De Filippis,
University and INFN Bari

15. Secondary vertex finding
The recursive secondary vertex finding algorithm:
fits all tracks to a common vertex, separates the incompatible tracks, stores the cleaned-up vertex if its χ2 is small enough, and searches for additional vertices in the set of tracks discarded in the previous iteration
Two parameters:  the cut on the prob. of compatibility of a track to a vertex
 the cut on the vertex fit χ2.
Bsmm
BsJ/ 
BsJ/ 
s(z) m
s(z) m
s(z) m
Bsmm
BsJ/ 
s(x) mm
47.5 ±3.63
55.3 ±0.95
s(z) mm
71.5 ± 1.3
72.7 ±1.4
CPU time msec
1.9 3
Siena May 23-26
N. De Filippis,
University and INFN Bari

16. Tracking for high level trigger
Track reconstruction for the HLT is guided by external information from a Level-1 Trigger or a HLT candidate
defined a region for track reconstruction
Regional seed generation
Limited to some region identified by Lvl1 objects (e.g. cone around  direction)
reduced
# of track seeds
# of operations per seed
Partial/Conditional Tracking
Stopped if :
N hits are reconstructed
PT resolution > given threshold
PT value < given threshold
Reduced amount of CPU time for trigger decision: 500 ms on a 1GHz machine and possibly 50 ms in 2007
Siena May 23-26
N. De Filippis,
University and INFN Bari
HLT Tracking does not need to be as accurate as in the offline

17. Partial track reconstruction for HLT
(barrel)
pT resolution
the full tracker performance
asymptotic accuracy is reached after only 5 or 6 hits.
The fake rate decreases to below the 1% for tracks with at least 6 hits.
The most commonly used stopping condition for HLT tracking is to limit the number of hits in a track to 5 or 6, provided the ghost track rate is acceptable.
Siena May 23-26
N. De Filippis,
University and INFN Bari

18. Performances of reco. in BS -+
@ L1:
2 trigger, PT  3 GeV, ||  2.1
@ High Level Trigger:
Regional tracking look for pixel seeds only in a cone around
the 2, with PT  4 GeV and d0  1mm, and compatible with PV
Conditional tracking reconstruct tracks from good seeds
Stop reconstruction if PT  4 5
Keep only tracks with σ(PT)/PT  2%, Nhit =6
If 2 Opposite Signs tracks found
Calculate the invariant mass
Retain pairs with a) |M-MBS|  150 MeV
b) Vertex 2  20 & d0  150 m
Lvl-1 e
HLT e
Global e
Events/ 10fb-1
Trigger Rate
15.2%
33.5%
5.1% 47
<1.7Hz
Siena May 23-26
N. De Filippis,
University and INFN Bari

19. Performances of reco. in BS -+
BS Mass resolution
HLT Full Tracking
 = 74 MeV
 = 46 MeV
Old offline analysis (hep-ph/ Jul 1999) predicts:
14 evts  2 90 C.L. with 20fb-1 (1 2x1033 cm-2s-1 )
5 observation with 40fb-1 and high lumi too
……… But L1 is in ||  slightly different kinematic cuts
Update foreseen for the CMS Physics TDR
Siena May 23-26
N. De Filippis,
University and INFN Bari

20. University and INFN Bari
Conclusions
The CMS Silicon Tracker has robust performance in a difficult environment
The pixel vertex detector allows fast & efficient track seed generation as well as excellent 3-D secondary vertex identification
A sufficient precision in track reconstruction is already achievable with the pixel hits and 4 silicon strip hits redundancy of the CMS tracker
the possibility to perform a “fast track reconstruction” is very useful for the High Level Trigger.
Siena May 23-26
N. De Filippis,
University and INFN Bari