Diapositiva 1

1
Impact of CMS Silicon Tracker Misalignment on
Track and Vertex Reconstruction
Nicola De Filippis
Department of Physics and INFN Bari
On behalf of Lucia Barbone INFN Bari Thomas
Speer University of Zurich Oliver Buchmueller,
Frank-Peter Schilling CERN Pascal Vanlaer
IIHE / ULB TIME05, Zurich, Switzerland, 3rd -
8th October 2005
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• Goals
• To evaluate the impact of tracker misalignment on
  track and vertex reconstruction
• Plan of the talk
• Sources of tracker misalignment
• Misalignment simulation and scenarios
• Effect of misalignment on
• Tracking efficiency and track parameter
  measurement
• Primary vertex reconstruction
• Vertex fitting

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• 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 lt 2.5.
• 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

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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 10-60 ?m, sz 500 mm
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• Unavoidable uncertainty on the exact positions of
  the silicon senson in the tracker due to
• The mechanical accuracy to position the
  individual silicon modules within each of the
  subdetectors (TIB, TOB, and TECs) is about 50 µm.
  
• The mechanical accuracy between the subdetectors
  will more likely be of the order of mm.
• The detector positional accuracy, estimated from
  Monte Carlo Simulation, needed to start the
  pattern recognition in the CMS silicon tracker is
  100 µm.

• Alignment procedures with the purpose
• to determine the absolute position of a
  sufficient number of mechanical support structure
  elements with a precision better than 100 µm in
  order to start the pattern recognition will
  be performed with the optical laser.
• to determine the positions of the detectors with
  an accuracy of 10 µm in order to reconstruct the
  track parameters. can be achieved by using
  sufficient statistics of reconstructed tracks
  (several days of data taking).

Those are the input for the misalignment
simulation and studies
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• The misalignment of CMS tracker is introduced
• by displacing the detector modules which host
  the reconstructed hits while leaving the local
  hits in place (so no need to generate events with
  a distorted CMSIM/OSCAR geometry)
• at various hierarchical levels, like for example
  at the level of misplacing the whole forward
  endcap or just one rod or detector module in the
  outer barrel
• Realistic estimates for the expected
  displacements of the tracking systems are
  supplied in input
• A software tool exists to simulate misalignment
  effects for all CMS tracking devices (and also
  muon system) in ORCA!

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• The hierarchical structure of the Tracker
• Tracker decomposed into various parts the
  inner/outer barrels and the barrel pixels, the
  endcap, mini endcap and pixels.

• Displacements implemented
• Rotation around x,y,z
• Shifts in x,y,z

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First Data Taking scenario ( lt 1 fb-1 ) Laser
Alignment Mechanical Constraints ?100 mm
alignment uncertainties

• Expected RMS values
• for of layers after Laser
  Alignment (used to generate random shifts at run
  start)

Small misalignment for pixel because a so large
number of tracks is expected to perform track
based alignment

• Expected RMS values for
  modules, rods, ladders, rings and petals

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• Expected RMS values for rods,
  ladders, rings and petals

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• Events single m, HZZee-mm-, ttH, DYmm-,
  BsJ/y j, Bsmm-
• ORCA_8_7_3 misalignment tools
• Standard track reconstruction (Combinatorial
  Track Finder)
• Tracking efficiency
• Track parameter resolutions
• Standard primary vertex reconstruction (Primary
  Vertex Finder)
• Vertex finding efficiency
• Primary vertex position
• Least-squares vertex fitter (Kalman Vertex
  Fitter)
• Position resolution, tails, bias, pulls

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• Selection
• track seeding, building, ambiguity resolution,
  smoothing with KF
• 8 reconstructed hits, simul. and reco. tracks
  share a 50 of hits
• Efficiency number of reco tracks matching simul.
  tracks / number of simul tracks
• - Simul. track pT 0.9 GeV/c, 0lthlt2.5 , tip3
  cm, lip30 cm, nhitgt0
• Reco. track pT 0.7 GeV/c, 0lthlt2.6 , tip120
  cm, lip170 cm, nhit8
• Fake Rate number of reco tracks not associatd to
  simul tracks / number of reco tracks
• - Simul. track pT 0.7 GeV/c, 0lthlt2.6 , tip 300
  cm, lip 300 cm, nhitgt8
• Reco. track pT 0.9 GeV/c 0lthlt2.5 , tip 3
  cm, lip 30 cm, nhit8
• Track parameters resolution sigma of Gaussian
  fit to distribution of residuals

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• In search for compatible hits, alignment error
  accounted for by default
• Key ingredient to recover full efficiency at high
  pT but it makes the fake rate larger
• Alignment error ?superstruct ? ?struct ?
  ?module(tables in slide 9-10)
• Added to error of reconstructed hit at track
  fitting

Full efficiency recovered when accounting for
alignment error
Single ? - pT 100 GeV Moderate
increase Alignment error correctly accounted for
Inefficiency when alignment error not accounted
for dip in TID region recovery in TPETEC
region due to small misalignment of TPE
In the region of h from 1.5 to 2 TOB are not
used but only pixel plus TIB and TID are used.
TID are misaligned of 400 m in the first scenario
and the effect on the efficiency is relevant.
For h gt2 TID are not used but only TPE (fully
efficient because the pixel misalignment is only
5 m in TPE and 10 microns in TPB ) and TEC so the
efficiency increases...
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• Average fake rate in ttH events pile-up
• Track multiplicity between 50 and 100.
• Fake rate 1.5 for perfect alignment and
  increases to 4.5 for short-term alignment
  scenario
• Fake rate decreasing as much as the number of
  rec hits used.

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Perfect alignment resol. 3 good agreement
with previous results Short-term 1 fb-1 resol.
6 curve reproduces tracker misalignment Long
term 10 fb-1 degraded by factor 1.4 wrt. perfect
alignment
pT residual/pT the central value is quite the
same 1.2 A factor 2 in RMS is observed in
the first data taking scenario, the mean is
shifted
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• Momentum resolution vs. pT, averaged in ?

? in H(300 GeV)?ZZ?ee?? Low luminosity Misalignmen
t affects high-pT more Multiple scattering
dominates below 10 GeV
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• d0 resolution vs. ?

• z0 resolution vs. ?

Pixel-dominated- Short-term only slightly worse
than long-term (same misalignment of pixel det.)
d0 and z0 resolution is fairly constant 9 mm
and is dominated by the hit resolution of the
first hit in the pixel detector
The improvement of the resolution up to a h0.5
can be attributed to the fact that in the barrel,
as the angle with which the tracks cross the
pixel layers increases, the clusters become wider
improving pixel-hit resolution
Long-term factor 2 degradation
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• f vs. ? cotq vs. h

Correlated with pT and d0
Correlated with z0
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• Muons from H (300)?ZZ?2e2m

• The mean values of Z mass with and without
  misalignment are in agreement.
• The variance of the fitted gaussian peak in the
  first data taking scenario is about 10 larger
  that the perfect alignment case.

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• Primary vertex finder algorithm proceeds in 4
  steps
• an initial track selection with cuts
• the significance of the transverse impact
  parameter d0/s(d0) is required to be smaller
  than a configurable value, 3 by default
• the track is required to be larger than a
  configurable value, 1.5 GeV/c by default.
• tracks are extrapolated to the beam line (x0,
  y0), and grouped according to their separation
  in z, in order to form primary vertex candidates.
  The maximum separation between two successive
  tracks belonging to the same primary vertex
  candidate is 1 mm
• each primary vertex candidate is then fit, and
  tracks incompatible with the vertex are discarded
  recursively, starting from the track with worst
  compatibility. Track removal stops when all
  tracks are compatible to more than 5 percent.
• a final cleaning of the vertex candidates is
  made. Vertices with a probability below 5 are
  rejected. Vertices compatible with x0, y0 to
  less than 1 are rejected.

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Vertex finding efficiency e defined as the ratio
of the number of events where the correct PV
vertex was found within Dz500 mm from the
simulated signal vertex divided by the total
number of events.

• for the primary vertex candidate nearest to the
  simulated signal vertex within that interval it
  is computed
• the position resolutions s the standard
  deviation of a Gaussian fit to the distributions
  of the residuals with respect to the simulated
  vertex position in x, y, z
• the bias, i.e. the average value of these
  distributions
• the tails, defined as the 95 coverage of the
  residual distributions. The
• fraction of events in the tails can then be
  evaluated by comparing the 95
• coverage to 2 s
• the precision of the fit covariance matrix,
  evaluated by the standard deviations
• of a Gaussian fit to the distributions of the
  standardized residuals in x,y,z. These
• standard deviations are further called pulls

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• Samples ttH, DY?mm-, BsJ/y j , low luminosity
  pile-up

• The effect of tracker misalignment on the
  primary vertex finding efficiency is small. The
  efficiency drop is max 3.5 (some vertices
  failing the selection cut on the compatibility
  with the beam axis)
• Drop identical in short-term and long-term
  Pixel-dominated

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Resolution significant degradation by 6-8 mm in
x,y,z Short-term, high pT misalignment of
silicon strip also plays a role
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• Evaluate the impact of misalignment on the fit of
  the vertices
• Pure vertices only rec tracks matched to the
  simulated tracks which were produced in the
  selected decay 4 tracks with low pT are fitted
  to a vertex
• KalmanVertexFitter (Least-squares) used to fit
  vertices

• Secondary vertex of B0sJ/y j 12 mm degradation
  in all coordinates
• Primary vertex of B0sJ/y j larger effect than
  with primary vertex finder (incompatible tracks
  not discarded)
• Pixel-dominated same observations as for
  primary vertex position
• so The misalignment significantly degrades the
  estimated positions, in terms of resolution and
  bias.

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• Track reconstruction
• global efficiency recovered if the Alignment
  error is combined with the error on hit used in
  the fit but the fake rate increase from 1.5 to
  4.5
• A factor 2 is observed in the RMS of the pt
  resolution for both single muons at pT 100 GeV/c
  and muons from H(300)?ZZ?2e2m.
• The Z mass computed as the di-muons invariant
  mass is 10 larger w.r.t perfect aligned case
• Vertex reconstruction
• Primary vertex efficiency 3.5 max of
  efficiency drop
• Primary vertex position significant degradation
  by 6-8 mm in x,y,z
• Vertex fitting 12 mm degradation in all
  coordinates

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• 1000 events OSCAR 3.6.5 / ORCA 8.7.3
• Bsmm- ( B.R.3.5x10-9) mass from reconstructed
  muons
• 2 methods GenID selected using MC info RecoID
  2 tracks with highest pT (pT gt 3 GeV/c)
• No kinematic fit bb back. rejected by cuts on
  invariant mass, seconday vertex reco, isolation

• GenID Perfect 46.4 MeV Short-term 50.0 MeV
  that is 9 Long-term 48.6 MeV
• RecoID Perfect 45.5 MeV Short-term 53.9 MeV
  that is 18 Long-term 49.5 MeV
• Impact of misalignment moderate no degradation
  of the CMS performance on this channel

GenID
RecoID
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• Algorithms are compared on the basis of their
  performance in
• finding the primary and secondary vertices, in
• producing ghost vertices from incorrect track
  associations, and in
• assigning the tracks to their vertex efficiently
  and with a good purity.

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• Samples ttH, DY?mm-, Bs?J/y f , low luminosity
  pile-up

• Some efficiency drop, max 3.5
• PV candidates become incompatible with beam line
  (cut at 1 compatibility)
• vertex error less well estimated (confirmed by
  Pull distribution)
• Drop identical in short-term and long-term
  Pixel-dominated
• Very little effect on track assignment

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• Resolution significant degradation by 6-8 mm in
  x,y,z
• Not like a convolution of independent Gaussians
• Correlated module shifts from structure
  misalignments account for a large part
• Biases related to shifts of Pixel half-barrels
  (cross-checked by selecting track subsamples)
• (dx, dy, dz) X (-1.6 / -9.2 / 7.5) ?m -X
  (23.9 / -11.8 / -0.6) ?m
• Short-term, high pT misalignment of silicon
  strip also plays a role

• Hits thought to be
• ?(dx, dy, dz) away from their true position

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• to derive the impact of the misalignment of
  tracking and muons detectors on the
  reconstruction and on the H?ZZ?ee mm channel
  study _at_ Low Luminosity
• to check different levels of effects
• single muon and electron track reconstruction
• L1 HLT selection
• Electron Identification (EleID)
• Lepton Tracker Isolation
• Signal to Background discrimination
• Higgs mass reconstruction from the di-lepton
  mass invariant
• Evaluation of Discovery Significance

Completed
On going
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• 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)

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• 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.

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• 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)
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• The drop of the efficiency in the region at h0
  is due to the gaps between the pixel
• barrel sensors, which are aligned every 6.4 cm
  and in particular at z0, and which cause some
  tracks not to have the two required pixel hits.

• At high pseudo-rapidity, the lack of coverage of
  the two pairs of forward/backward pixel disks
  causes a slow degradation of eff.

h
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• The pT resolution is better than 2 for pT lt 100
  GeV/c up to ?1.75 at large ? 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
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Radiation lengths of tracker
Interaction lenght of tracker
.killing tracks
A lot of material!
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• 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

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• 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 time50msec _at_1 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
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• The recursive secondary vertex finding algorithm
• fits all tracks to a common vertex, separates
  the incompatible tracks, stores the cleaned-up
  vertex if its ?2 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 ?2.

Bs?mm
Bs?J/? ?
s(z) ?m
s(z) ?m
s(z) ?m