Tracking Review

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Tracking Review SVT - May 2000
Helen Caines For the SVT Software Group
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Software Overview

• The Software road map
• The raw-data -gt sequences
• Cluster Finding
• Cluster de-convolution
• Cluster Fitting
• Tracking
• Method 1 Grouper technique
• Method 2 Point-point technique
• dE/dx

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SVT - Details
The SVT A wafer is 6.3 cm x 6.3 cm area, 300
mm thick - 0.3X0 Average radiation length seen
by a particle if 4.5X0 incl. fee cards
etc. Consists of 216 wafers 3 barrels Inner
barrel has 8 ladders 4 wafers/ladder
Middle barrel has 12 ladders 6
wafers/ladder Outer barrel has 16 ladders
7 wafers/ladder Resolution 20 mm
Outer radius 15cm Middle Radius 10cm Inner
radius - 6cm Length - ?21cm
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SVT Details (2)
Year 1 ladder at 12 0Clock position Middle
Barrel. 7 wafers on the ladder. Using to
evaluate Pedestal code, zero suppression,
calibrations, and cluster finding
Support rods
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SVT Software Map
Raw Data
Cluster Finding
Grouper Tracking
Sequence Adjusting
Slow Sim
Local-Global
De-convolution
Calibration
dE/dx
Point-Point Tracking
Cluster Fitting
Fast Sim
Vector-Point Matching
Vector-Vector Matching
Database
Global
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Calibrations and the Year 1 Ladder
First Time bucket
Other 127 Time buckets
Anode
You can see the edges of the 15 PASAs and more
obviously the 3 analogue buffers where the
multiplexing occurs
M.Munhoz
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Pedestal Subtraction
Have noise at 1st capacitor and in 1st time
bucket 1st capacitor is more of aproblem
because it is in a random position each event.
1st time bucket doesnt contain data
You can see the first time bucket noise and the
first capacitor glitch
M. Munhoz
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Drift Velocity Calibration
SDDs modeled using 2 drift velocities. One in
the drift region and one in the focusing region
There is a temperature dependence across the
wafer which must be accounted for.
Residuals as a function of drift distance from
E896 data
Havent quite got focusing region correct
S. Pandey
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Online Monitor
First Hit-Track matching in STAR!!!!
Take tracks from TPC. Project to Year1
ladder. Identify hit in correct location.
March 2000 Cosmic data
M. Munhoz
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Slow Simulator

• Steps towards a simulator
• Given a dE and hit position generate hit.
  Initially a gaussian s20mm
• Width at anodes increases due to diffusion.
  Symmetric in drift and anode directions. s(t)
  ?2Dt
• Get drift time from database
• Width at anodes increases due to coulomb
  repulsion.
• Add in white noise from the electronics before
  PASA
• Split between anodes
• PASA response function Gain and shaper
• Split between time buckets
• Write out raw data

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Slow Simulator (2)
Noise
Signal
Sum
Noise as measured by Year 1 ladder
S. Bekele
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The PASA response function
After passing through the PASA the signal in the
time direction is no longer gaussian, the
Laplace transform of the response function is
Where ts11.5ns, tl 500ns
In the time domain this has the extended form
Where a 1/ts and b 1/ tl, and c b-a
Peaking time 100ns Width 50 ns
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The PASA response function (2)
Fitting the PASA response function to real (many
times) MIP hits. You can see a) the fit is good
b) the broadening of the hit as the drift time
increases.
E896 G Lo Curto
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Sequence Finding

• A sequence is a chain of pixels in the drift
  direction which are above a given ADC threshold
• Sequence finding is done in two steps
• For year 1 have to make all sequences and do
  zero suppression ASIC code simulation
• Then do second pass at sequence adjusting Will
  even do this on zero suppressed data.
• This is a new technique developed for E896
• Helps dig out the signal from the noise,
  especially at long drift where the signal/noise
  ratio gets low.

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Sequence Finding(2)
Assumes noise is white noise and no
auto-correlation. This has been looked at in
pulser events and believed to be true Takes into
account not only the ADC value of the current
pixel but also of its neighbours in time
direction. Take 3 pixels p1,p2 and p3 Define the
quantity Eval (p2) 1/(P(p1)P(p2)P(p3)) Where
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Sequence Finding (3)
So P(adci) is the probability for a pixel at
index i in a given sequence to have an adc value
greater than adci assuming a gaussian
distribution of standard deviation of around 2 or
3 counts. For a count of zero this probability is
0.5 and for negative counts it is bigger. With
increasing ADC counts P(adci ) gets smaller and
smaller. In fact for ADC counts above 13 the
probability is 10E-10. This means the inverse
probability (Eval) is small for small counts
(below or up to the mean count generally) and big
for large counts. Since three consecutive time
bins in are considered for each pixel in a
sequence, if the middle pixel has a large count
and the adjacent ones have small counts, then the
product of the respective inverse probabilities
which corresponds to the middle one will be very
small. This allows us to eliminate some spurious
pixels due to noise spikes that would pass a more
usual two threshold cut
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Sequence Finding (4)
ADC
Average count for a MIP
timebucket
Noise
Red area Prod(ADC0) 0.5 Green area
Prob(ADC4) 0.008 Blue area -
Prob(ADC10) 10e-7 X 3 neighbouring pixels,
take inverse to calc eval.
Real hits
Threshold
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Sequence Finding (5)
So we cut on eval(pi). What threshold to set?
Offset purity with efficiency.
Expect a MIP to be 60 mV at longest drift
Want to put the threshold 108. Best efficiency
and purity
1 ADC count 4 mV
G. Lo Curto
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Sequence Finding (6)
Evaluator as function of drift distance for real
and pulser events
Evaluator for real and pulser events
Log Scale
End of drift region
Cut here
Real E896 Data
G. Lo Curto
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Cluster Finding
The cluster finder search starts with the first
sequence from the first anode with a sequence on
it. This sequence is considered as the first
member of a cluster. The finder then performs the
following actions 1) It tags this sequence and
looks at sequences on the immediate right and
left anodes. Whenever a new adjacent sequence is
found, it is tagged and a record of its sequence
number and the corresponding anode number is
kept. 2) While tagged members on left and right
are ignored,the process in (1) is repeated for
each one of the newly found members in a search
for other new sequences. This continues until no
further new members are found. At which point the
cluster finder says " the first cluster is found
,it is time to look for the next one... " 3) the
finder goes back to the first anode and searches
for a sequence which is not tagged. Steps (1)
and (2) are repeated until all sequences have
been tagged Note If the anode numbers are not
consecutive while looking to the left of a given
a node, the anode is marked so that subsequent
searches for untagged sequences start there.
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Cluster Finding (2)
Does it work?
Raw Data Colour coding is ADC value
Clusters Colour coding is cluster number
Note Cluster Finder does not try to decide of
clusters are merged
S. Bekele
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Cluster Finding (3)
E896
Peak amplitude drops as drift time lengthens due
to diffusion etc
Integrated charge is however constant as a
function of drift time No charge loss in
detectors or cluster finding and fitting.
J. Takahshi
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Cluster De-convolution
De-convolution Being worked on currently -
adaption of E896 code. Looks for peak-valley
ratio to determine if cluster is a convolution or
not. However cluster merging in the SVT is not a
big problem
Barrel Clusters per Wafer Sequences per Wafer Pixels per wafer Pixel occupancy
Inner 80 275 1137 1.9
Middle 32 114 475 0.8
Outer 19 66 270 0.4
Average 32 113 468 0.8
Calc. from standard Hijing events
D. Read
i.e. an average hit covers 15 pixels, 3 anodes,
5 time buckets
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Cluster De-convolution
If peak to valley ratio is gt 50 considers it has
found a new cluster. The fitting is via moments
analysis again but only the 9 pixels surrounding
the peak are considered. Hits are flagged to
indicate they have been de-convoluted
0 0 0 0 0 0 0 0
0 0 0 0 1 1 2 0 0
0 0 0 4 2 2 0 0
0 0 0 6 21 14 0 0 0
2 1 23 39 17 0 0 2 2
2 3 14 7 0 0 2 21 18
2 0 -4 0 0 12 36 39 6
0 0 0 0 2 9 11 -1 0
0 0 0 -3 -4 -4 0 0
0 0 0 0 0 0 0 0 0
0
Errors on hits scaled to reflect the separation
of the hits. Larger the peak-to-valley ratio the
smaller the errors
De-convolutor forms two hits with peaks put where
green dots are.
S. Pandey
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Cluster Fitting
Local Position in Time bucket and anode position
calculated via a moments analysis . Causes a
shift because of the PASA response. The shift
gets larger as drift and hence width of signal
gets wider. Can be corrected analytically. Fitting
to PASA response too slow.
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20
0
0
3 cm
D. Read
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Local-to-Global Conversion
Guts of the Local-to-global conversion is there.
Need interface to database. Need data in
database. Drift vel. crucial here. As is
geometry of SVT. T0 information also required
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Grouper Tracking
Grouping Technique (finder only) If one assumes
straight lines for the tracks instead of helices
a trivial mapping in f-j from the primary vertex
places all hits on a track into the same
location. For a particle with pt 100MeV/c in a
0.5T field f(R15cm) - f(R5cm) 5.10 So we
need bins of close to 50 so most tracks have all
their space points within a f bin If you iterate
increasing the binning for hits you move to
lower and lower pt (or larger radii of
curvature). Advantagethis method is fast.
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Tracking via grouping
For primaries this technique has been shown to be
over 94 efficient, and for pt gt200MeV/c the
efficiency 97 when using the SVT alone. Colour
coding Blue SVT Yellow SSD Green
TPC Red lines Tracks from grouper
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SGR - Primary and Secondary Efficiency Low Mult
100 Tracks/event
40 Tracks/event
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SGR - Primary and Secondary Ghosts Low Mult
100 Tracks/event
40 Tracks/event
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Tracking via grouping Current work
Currently work by the SSD group to add in the 4th
layer Work is about to start in converting this
code to c. Makes it more maintainable and
faster as only need to look at bins where there
are counts, using linked lists. Current fortran
routines have static arrays. Bad in 2 ways for
empty events waste a lot of time Searching in
empty bins. For REALLY large events can over
spill array boundries
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Tracking via Point-to-Point Method (1)
Disadvantage of the grouping technique is you can
only find primaries, or tracks appearing to
originate from the primary vertex. So we have a
standard follow your nose tracker which tries
to identify secondary tracks and those tracks
with too low a pt to be successfully identified
by the grouping technique. There is a primary
search loop where knowledge of the Primary vertex
location is used and then a secondaries loop
where tracks are no longer constrained to point
towards the main vertex
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Tracking via Point-to-Point Method (2)

• It starts at the primary vertex.
• Takes a point on the first barrel
• Using straight line projects to the 2nd barrel,
  finds closest hit within a search cones.
• Projects to next barrel, finds closest hit - up
  to 4th barrel
• In each projection the cone angles in x,y and z
  are settable.
• All 3 (or more) hit candidates for that hit are
  identified. A helix fit is done for each track.
  Best fit is selected as the track
• Hits are removed from pool and iteration starts
  with next hit

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Primary Efficiencies
100 Tracks/event
1200 Tracks/event
P. Fachini and D. Alvarez
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Primary Ghosts
100 Tracks/event 1200
Tracks/event
P. Fachini and D. Alvarez
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Secondary Efficiencies
40 Tracks/event
400 Tracks/event
P. Fachini and D. Alvarez
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Secondary Ghosts
400 Tracks/event
40 Tracks/event
P. Fachini and D. Alvarez
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Tracking Fitting (1)
x(t) x0 RHcos(F0 ht cosl/RH) cosF0
y(t) y0 RHsin(F0 ht cosl/RH) sinF0
z(t) z0 t sinl
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Track Fitting (2)

• Fitting is done by splitting the helix into 2
  parts
• A circle in the x-y plane
• A straight line in the s-z plane
• The assumption is pretty good due to the
  homogeneity of the B-field
• Can choose to fit as primaries (include the
  primary vertex) or as
• secondaries and use only the SVT/SSD points
• The circle fit uses a conformal mapping of x-y to
  u-v such that
• u x/(x2 y2), v y(x2 y2)
• This only works if one of the points is close to
  the origin, force this
• by translating all points to x x-xv and y
  y-yv
• So with 0,0 being on the circle
• R2H (x-xH)2 (y-yH)2
  v a(1) a(2)u

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Momentum Resolution Primaries Std Mult
Mean-0.01 s 0.22
pt
s
Mean
pt
pt
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Momentum Resolution Secondaries Std Mult
s0.26 Mean -0.01
pt
s
Mean
pt
pt
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Tracking with the Year 2 detectors
Primaries
Secondaries
0
1 GeV
1GeV
0
Old results Similar to current ones - Good
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Efficiency as a function of Primary vertex
location
1070 Tracks/ event
P. Fachini
860 Tracks/event
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Efficiency as a function of Primary vertex
location
420 Tracks/ event
P. Fachini
380 Tracks/ event
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Tracking with the SVT
Problems/Future Momentum resolution not too good
Could improve primary resolution by including
vertex in fit, how to tell primaries from
secondaries? SGR and STK fail slightly with
inclusion of SSD See Lilians talk later for
possible solution Tracking efficiency gets worse
as primary vertex moves from z0 Do we care if
we cant track at z-15cm, which is nearly
outside of the SVT anyway? Not in the beginning I
dont think may be useful to do this at a later
date but have the FTPCs there so not sure Can
reject these events either online with L3 or off
line using a vertex finder. Doesnt have to be
highly accurate just approximate. There already
exist several fast vertex finders (SVT and FTPC)
that work with just space points No need to do
tracking. Sure TPC can do the same Want to move
point-by-point tracker (if we keep it) to c.
Fortran code hard to maintain. Not top
priority. SSD group are exploring using a Neural
Net approach to find low momentum tracks which is
where our current trackers all break down.
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dE/dx
Currently a c code exists. Needs some work as
uses both SVT and SSD as if the hits are the
same. Problem is gain and dE not the same For
different detectors. Not even the same for the
SVT individual wafers. Need to add in some
ability to normalise wafer dEs so get to The
same mean dE/dx on all wafers for a given
particle and momentum. Cluster finder method
allows dE/dx to be performed (finds correct
clusters with good amount of charge) from E896
beautiful results
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dE/dx
d
p
t
k
p
dE/dx with SVT
Positive Tracks from E896 J Takahashi
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Time Plan May 2000 - Feb 2001
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Integrated Tracking Methods with the Year 2
detectors

• Two methods
• Track-Track matching between TPC and vertex
  detectors
• Form tracks independently in the SVTSSD and
  the TPC.
• Then project all tracks to a given radius and
  match vectors
• Track-Space point matching between TPC and vertex
  detectors
• Project the TPC to individual barrels and
  match the closest space-point within given
  constraints.

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Tracking Matching between SVT/SSD and TPC
Take all tracks from SVTSSD and tracks from
TPC. Project tracks to a common radius. Form a
footprint of each track at that radius, size of
footprint dependant on errors from track fit and
a gross estimate of the material the track as
passed through. Match best pairs of tracks. We
take advantage of the this step and have VERY
loose cuts in the SVTSSD tracking. This means we
pass many fake tracks to the matcher. The matcher
then weeds these bad tracks out. i.e the SVT
tracking tries to get a high efficiency at the
expense of purity.
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Tracking Matching between SVT/SSD and TPC
Track-Track matching SVTSSDTPC Primary Fin
dable 1743 Correct 1366 - 78 Ghost 158
- 10
Secondary Findable 252 Correct 71 -
28 Ghost 31 - 30
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Tracking Matching between SVT/SSD and TPC
Problems Not all geometry in correctly Errors
not correct before propagation Efficiency of
matching low Need to find new, better radius to
match now have 4th layer. Should it change if
there isnt a 4th layer hit?
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Upgrades/ Future work
Speed!!!! Integrate space point to track
matching with grouper technique Take out the
easy to find high mtm tracks using a fast method
then apply track-hit matching The improvement of
the secondary reconstruction is counterbalanced
by the increase in ghost contamination Integrate
dE/dx into the hit matching from SVT and SSD Take
into account the material passed through by the
track. Take advantage of kalman /propagation
(Geane/other?) work being done for year 1.
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(No Transcript)
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Space Point Track Matching
Takes 5 passes At least 1 hit in each layer At
least one hit in each layer with larger search
cone At least one is in 3 different layers At
least one hit in 2 different layers At least one
hit in the SSD In each pass there are 7
iterations over pt thresholds (high pt
first) Project to SSD, find hit, refit track,
mover to next barrel
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Track-Hit Matching Efficiency
0
1.5
-1
1
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Tracking with the Year 2 detectors Method 2
Secondary Findable 252 Correct 71 -
28 Ghost 31 - 30
Track-Space point matching Note there are now
more findable hits as allow as few as 1 hit per
track Primary Findable 1778 (1743) Correct
1399 (1366) - 78 Ghost 263 (158)
- 16
Secondary Findable 333 (252) Correct 202 (71)
- 61 Ghost 90 (31) - 31
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SSD Details
The SSD Double sided silicon strip detectors 16
wafers per ladder Stereo angle 35 mrad pitch 95
microns. Detector size is 7.5cm x 4.2xm 300
microns thick. Resolution is 15 microns in r
700 microns in z radiation length of 1 ladder is
0.7X0