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o
Silicon only track �nding - current developments
and outlook
Jakob Lettenbichler, Rudolf Frühwirth
Institute of High Energy Physics
Austrian Academy of Sciences
July 19, 2012
Jakob Lettenbichler, Rudolf Frühwirth 1 HEPHY Wien & BELLE Collaboration
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Outline
current state of the TF (overview)
current feature-set, some words to
sectors
Hop�eld network without Kalman �lter
ghost hits and secondary particles
performance
next steps (release)
Jakob Lettenbichler, Rudolf Frühwirth 2 HEPHY Wien & BELLE Collaboration
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O Segment finder - 2-hit filterfilters by distance, min&max, including virtual Segment
Cellular Automatonevolving states, includes TC-collector
Hopfield Networkuses QI's to find best subset among overlapping TC's
CleanTC'sKalman filter
not implemented yet
O Post 4-hit filterfilters by zigZag, ΔpT
O Neighbour finder - 3-hit filterfilters by angle and Δ-distance min&max
O Sector setup - 1-hit filterfilters by set of compatible sectors, allows momentum dependent setups
- The arrows represent a schematic interpretation of the possible number of combinations of hits at that point- Filters marked with an O use external information generated by simulation
Schematic view of the low momentum track finder in Belle II
Unsorted hits from tracks, background, ghost coming from an event
Jakob Lettenbichler, Rudolf Frühwirth 3 HEPHY Wien & BELLE Collaboration
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Sectors
Motivation using sectors:
gradually �ltering reduces combinatorics → cuto�-list needed
windmill structure and slanted sensors forbid simple
layer-wise cuto�s → at least sensor-wise cuto�s
quality of chosen cuto�s is essential:
to loose → more ghosts
to narrow → lose real tracks
what about momentum dependency?
Jakob Lettenbichler, Rudolf Frühwirth 4 HEPHY Wien & BELLE Collaboration
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Many ready to hand-advantages using a sector map:
subdividing sensors in sectors leads to customized cuto�s
improving cuto� quality by storing compatibility-lists
(including individual cuto�s) for each sector
this leads to pretty fast �ltering by simply sorting hits into
their sectors → only compatible sectors are checked for
hit-combinations
allows momentum dependent sector setups (especially
important for distinction between �high� momenta
>70MeV/c and �low� momenta below 70MeV/c and curling
tracks as well)
sector size can be adjusted easily when switching between
setups (when requested)
Jakob Lettenbichler, Rudolf Frühwirth 5 HEPHY Wien & BELLE Collaboration
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dZ
Layer X+1
Layer X
IP
Track
Sector B
Sector A
−8 −6 −4 −2 0 2 4 6 80
0.05
0.1
0.15
0.2
∆
−8 −6 −4 −2 0 2 4 6 80
0.2
0.4
0.6
0.8
Z between 2hits of arbitrary track passing layer X&X+1 in [cm]
Z between 2hits of arbitrary track passing sector A @ layer X & sector B @ X+1 in [cm]
∆
Jakob Lettenbichler, Rudolf Frühwirth 6 HEPHY Wien & BELLE Collaboration
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Hop�eld network
Basic principle
searches for non-overlapping subset of track candidates
this represents a combinatorial optimization problem, where
minima represent good (local) or the best (global) solution
track candidates represented by neurons having a state
comparable to state of cells within cellular automata
state evolves when iterating through time-steps, where theupdated state depends on several aspects:
their old state (compare to markov-chain)
the compatibility of two randomly chosen neurons
their quality indicators (QI, normally χ2-value, now track
length), static value
and a thermal noise term to avoid local minima of the
optimization problem, decreases with each time-step
Jakob Lettenbichler, Rudolf Frühwirth 7 HEPHY Wien & BELLE Collaboration
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Trap when using track length as QI
when using track length as QI, several TC's carry exactly the
same value (practically not possible when using a χ2-value)
this e�ectively means that local and global minima are
surrounded by quite �at plains
thermal noise overcomes this by adding arti�cial
perturbations, but: e�ect decreases with each iteration
therefore: e�ect of �atness between minima increases
dramatically since the QI is static but the noise is not
result: since only neurons whose state is above a chosen
threshold value are allowed to survive this �lter, the system
dies among the plain → all overlapped TC's get kicked
unexpectedly, this e�ect is more severe when looking at
�easy� setups like 10 tracks without background and ghost
hits, where ∼ 20% of all tracks are lost
Jakob Lettenbichler, Rudolf Frühwirth 8 HEPHY Wien & BELLE Collaboration
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Solution:
smear QI, even tiny changes are su�cient (but relying on
rounding errors is not enough) to practically annihilate this e�ect.
Table: Comparison between CA-only (TCC) and hop�eld results (w,
w/o bug). pT @ 0.06 - 0.07 GeV/c , SVD only
type of result post-TCC Hop�eld w bug Hop�eld w/o bug
clean 99.4% 81.8% 96.9%
cont. 0.0% 0.2% 0.2%
lost 0.6% 18% 3%
rectot 99.4% 82.0% 97.0%
TCrate∗ 1.37 1.00 1.00
∗: TCrate: number of TC's per number of reconstructed real tracks, ideal
value is one TC per track, when e�ciency is 100%, 1.2 means 20% spare
tracks. Includes ghost tracks and tracks found more than once
Jakob Lettenbichler, Rudolf Frühwirth 9 HEPHY Wien & BELLE Collaboration
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Simulation setup
1000 events with 10/20 tracks per event (muons), r3290
φ between 0 and 2π uniform, θ between 20◦ and 145◦
uniform
vertex (0|0|0), imports 1D&2D Clusters
standard GEANT4 setup, except wenzel model
low momentum setup, no curling tracks:
pT @ 0.06 - 0.07 GeV/c (SVD = 3L & PXD+SVD = 5L)
(0<r<12.5cm): Bz = 1.5T, (12.5cm<r): Bz = 0
high momentum setup, no curling tracks:
pT @ 0.07 - 0.1 GeV/c (SVD = 4L & PXD+SVD = 6L)
(0<r<15cm): Bz = 1.5T, (15cm<r): Bz = 0
BGcase 1: real tracks only
BGcase 2: adding ME particle and ghost hits
Jakob Lettenbichler, Rudolf Frühwirth 10 HEPHY Wien & BELLE Collaboration
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Table: chosen setup: VXD high (6 layers), 10&20 tracks per event, both BGcases
type of result 10 T 20 TBGcase1 BGcase2 BGcase1 BGcase2
TCC FNL TCC FNL TCC FNL TCC FNLclean 100% 98.3% 99.9% 86.4% 100% 99.4% 99.8% 76.3%cont. 0% 0.2% 0.1% 8.3% 0% 0.2% 0.2% 13%lost 0% 1.6% 0% 5.3% 0% 0.4% 0% 10.7%rectot 100% 98.4% 100% 94.7% 100% 99.6% 100% 89.3%
TCrate 1.46 1.00 2.41 1.13 1.47 1.00 3.93 1.34
Table: chosen setup: VXD low (5 layers), 10&20 tracks per event, both BGcases
type of result 10 T 20 TBGcase1 BGcase2 BGcase1 BGcase2
TCC FNL TCC FNL TCC FNL TCC FNLclean 99.6% 96.5% 99.4% 71.8% 99.3% 96.7% 99% 52.1%cont. 0.1% 0.5% 0.3% 18.1% 0.2% 1% 0.6% 27.2%lost 0.3% 34% 0.3% 10.1% 0.5% 2.3% 0.4% 20.8%rectot 99.7% 97% 99.7% 89.9% 99.5% 97.7% 99.6% 79.2%
TCrate 1.39 1.01 3.69 1.11 1.52 1.01 8.52 1.29
Jakob Lettenbichler, Rudolf Frühwirth 11 HEPHY Wien & BELLE Collaboration
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Table: chosen setup: SVD high (4 layers), 10&20 tracks per event, both BGcases
type of result 10 T 20 TBGcase1 BGcase2 BGcase1 BGcase2
TCC FNL TCC FNL TCC FNL TCC FNLclean 99.4% 96.9% 99.2% 82.5% 99.3% 98% 99% 69%cont. 0.0% 0.2% 0.2% 10.5% 0.1% 0.7% 0.4% 17.8%lost 0.6% 3% 0.6% 7% 0.6% 1.3% 0.6% 13.2%rectot 99.4% 97% 99.4% 93% 99.4% 98.7% 99.4% 86.8%
TCrate 1.38 1.00 2.59 1.16 1.39 1.00 4.67 1.41
Table: chosen setup: SVD low (3 layers), 10&20 tracks per event, both BGcases
type of result 10 T 20 TBGcase1 BGcase2 BGcase1 BGcase2
TCC FNL TCC FNL TCC FNL TCC FNLclean 94% 91.5% 94% 64.6% 94% 89.6% 93.8% 45.6%cont. 0% 0.2% 0.1% 2.3% 0.1% 0.3% 0.2% 3.5%lost 6% 8.3% 6% 33% 6% 10% 6.1% 50.9%rectot 94% 91.7% 94% 67% 94% 90% 93.9% 49.1%
TCrate 1.18 1.02 3.52 1.52 1.27 1.04 8.64 2.34
Jakob Lettenbichler, Rudolf Frühwirth 12 HEPHY Wien & BELLE Collaboration
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Table: chosen setup: SVD low (3 layers), 15 tracks per event (500 events),
BGCase2. 350 SVD cluster-combinations per event. TF no Curler, Events having
curlers
type of result 10 TBGcase2
TCC FNLclean 99.7% 77.6%cont. 0.2% 14.5%lost 0.1% 7.9%rectot 99.9% 92.1%
TCrate 5.32 1.31
Jakob Lettenbichler, Rudolf Frühwirth 13 HEPHY Wien & BELLE Collaboration
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Jakob Lettenbichler, Rudolf Frühwirth 14 HEPHY Wien & BELLE Collaboration
Outline TF overview Current state Performance Next steps The End
Jakob Lettenbichler, Rudolf Frühwirth 15 HEPHY Wien & BELLE Collaboration
Outline TF overview Current state Performance Next steps The End
Jakob Lettenbichler, Rudolf Frühwirth 16 HEPHY Wien & BELLE Collaboration
Outline TF overview Current state Performance Next steps The End
Jakob Lettenbichler, Rudolf Frühwirth 17 HEPHY Wien & BELLE Collaboration
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personal ToDo list for current meeting
�nalizing interface speci�cations
what shall I feed the track �nder with? (clusters or hits, what
about nonorthogonal slanted parts (ghosthits)?
what shall it produce?
any plans for momentum range (distinction between global
track �nding using CDC and SVD-only approach)?
Long-term and short-term goals
is there an easy-to-use documentation for using real
background samples (what about E-deposit, already useful
info in clusters)?
what about VXD-support, needed in fw version?
fw plans for time frames for SVD and PXD? how to
combine, what about rolling shutter, etc?
reconstruction speed − how many events per second shall be
processed in worst case scenarios?
Jakob Lettenbichler, Rudolf Frühwirth 18 HEPHY Wien & BELLE Collaboration
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Steps towards �rst FW release
separating TF and analysis elements (so far they are within
the same module)
implementing standardized interfaces for in- and output
check and adapt behavior during realistic background
situations
various usability optimizations
Med/Long-term feature requests for FW version
Kalman �lter
curling track support
tuning
Jakob Lettenbichler, Rudolf Frühwirth 19 HEPHY Wien & BELLE Collaboration
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that's all, folks!
Any suggestions, ideas or requests?
Jakob Lettenbichler, Rudolf Frühwirth 20 HEPHY Wien & BELLE Collaboration
