Vertex reconstruction framework and its implementation for CMS

1
Vertex reconstruction frameworkand its
implementation for CMS
R.Frühwirth, W.Waltenberger, HEPHY-Vienna T.Speer,
K.Prokofiev, Zürich University P.Vanlaer,
IIHE-Brussels University CHEP 2003, La Jolla, San
Diego, March 24-28

• Outline
• Introduction
• Vertex fitting
• Vertex finding

2
Introduction

• Vertex reconstruction can be decomposed in
• Vertex finding
• given a set of tracks, separate it into clusters
  of compatible tracks, i.e. vertex candidates
• inclusively not related to a particular decay
  channel
• search for secondary vertices in a jet
• exclusively find best match with a decay
  channel
• general solution requires generation of
  combinations, selection of topologies and
  kinematic constraints
• work in progress, not described here
• Vertex fitting
• find the 3D point most compatible with a set of
  tracks
• constrain track parameters with vertex

3
Motivation for a framework

• Problem is complex
• cant guess what the optimal algorithms will be
• there is probably not 1 optimal algorithm but
  several, each optimized for a specific task
• Math is complex but localized in a few places
• ease development by providing mathematical
  toolkit
• Performance evaluation is not easy
• comparison with Monte-Carlo truth not trivial
• vertex are high level reconstructed objects,
  i.e. made out of reconstructed tracks
• disentangle effects from track and vertex
  reconstructions
• Problem is very generic once tracks are given
• a good case for code re-use
• we need a flexible framework for the development
  and evaluation of algorithms

4
Vertex fitting
5
Problem definition
1 RecVertex 3D point most compatible with input
tracks
Vertex fitting
Bunch of tracks

• Principle minimization problem
• Find x which minimizes a function Fx f(pi),
• pi parameters of track i
• Example
• f(pi) xi
• p.c.a. to vertex
• F ?i1N (x-xi)T Ci-1 (x-xi)
• usual total ?2
• Algorithms may differ by
• choice of track parametrization pi (and function
  f(pi))
• form of function F to minimize

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Track parametrizations

• All parametrizations needed are supported
• provided by a concrete class
• LinearizedTrack
• computed on demand
• by helper classes
• cached for performance
• conversions from 1 parametrization into another
  also supported
• 2 parametrizations used in ORCA
• (x, y, z) at p.c.a. to vertex (previous picture)
  
• V.Karimäki, CMS Note 1997/051
• 5 parameters at perigee
• (q/pT, ?, ?p, signed d0, zp)
• P.Billoir et al., NIM A311(1992) 139
• R.Frühwirth et al., Computer Physics Comm. 96
  (1991) 189

7
Linearization

• LinearizedTrack why this name?
• f(pi) must be linearized in vicinity of true
  vertex
• 2 linearizations used in ORCA
• straight line track approximation, constant
  track error matrix
• used with p.c.a. parametrization
• helix track approximation, linear error
  propagation
• used with perigee parametrization
• Jacobians for error propagation also provided by
  LinearizedTrack
• helix model formally much more precise
• both models valid in our pT range (gt 0.7 GeV/c)
• requires first guess of vertex position
  linearization point
• abstract LinearizationPointFinder class
• 3 implementations in ORCA (1 non-robust, 2
  robust)
• based on crossing points of high pT track pairs

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Iterative vertex fitting

• Iterations arise naturally
• 1) when linearization point too far from fitted
  vertex
• 2) when function F has no explicit minimum
• To solve case 2), tracks should be allowed to
  contribute to vertex fit with weights ? 1
• see robust algorithms in Wolfgang Waltenbergers
  talk
• weight function of distance between track and
  current vertex
• evolves during iteration
• the same LinearizedTrack can contribute with ?
  weights to different vertices
• ? concrete VertexTrack class knows its
  LinearizedTrack, current vertex and weight
• Memory management of LinearizedTrack and
  VertexTrack by reference-counting mechanism
  (ref.-counting pointers)

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Kalman fitting formalism

• Error matrices of track parameters pi are
  uncorrelated
• VertexTracks can be added 1 after another to
  vertex
• update of vertex, in Kalman language
• abstract VertexUpdator
• 1 implementation per track parametrization
• VertexUpdator uses VertexTrackCompatibilityEstima
  tor to increment vertex fit ?2
• also, 1 implementation per parametrization
• can be used during vertex finding to test
  compatibility
• One more component
• VertexSmoother
• computes track parameters constrained with
  vertex position
• stores them in VertexTrack
• currently, implementation only for perigee
  parametrization

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Vertex finding
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Vertex finding framework

• Vertex finding class framework still in an early
  stage
• Users use an implementation of a
  VertexReconstructor
• Decomposition of VertexReconstructor still
  evolves while features common to new algorithms
  emerge
• Current decomposition
• 1) initial track selection FilterltRecTrackgt
• operates on each element of RecTrack container
• boolean result track accepted or rejected
• 2) VertexSeedGenerator
• finds clusters of compatible tracks
• 3) and one of the VertexFitters to fit each
  cluster into a vertex
• CombinationGeneratorltTgt, in ORCA statistical
  toolkit
• I.e. for exclusive vertex finding
• but performance analysis framework is well
  advanced

12
Analysis of performance
We want to evaluate, in b-jets, 50 GeV, ? ? 1.4
PV finding efficiency
SV finding efficiency
PV track purity
SV track purity
PV track assignment efficiency
for these algorithms
SV track assignment efficiency
1-fake rate
Total score
13
Comparison with MC truth
Association
Selected simulated vertices
Reconstructed vertices

• VertexAssociator
• by tracks
• uses TrackAssociator
• by distance

14
Evaluation of performance

• For each performance figure, 1 estimator class
• Examples
• VertexFindingEfficiencyEstimator
• VertexTrackAssignmentPurityEstimator
• updated each event
• These are all combined into a standard
  performance test
• VertexRecoPerformanceTest
• which reports results for each estimator, and a
  total Score
• Score is a user-defined function of the different
  estimators
• Example S Eff.PVa Eff.SVb Purity PVc
  Purity SVd
• (1-Fake Rate)e

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Vertex fast simulation

• VertexFastSim package
• Fully controlled input to vertex reconstruction
• Configurable event generator
• number and position of vertices
• number and momentum vector of prongs
• Very simple track reconstruction
• Gaussian smearing configurable resolutions
• fraction of non-Gaussian tails configurable
• What for?
• Test statistical consistency of vertex fitters
• Compare vertex finders for standard events
• ? speed-up development and debugging
• ? software release tests independent of full
  track reconstruction
• Future interface to FAMOS (see Stephan Wynhoffs
  talk) for more realistic yet fast track
  reconstruction

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Tuning of vertex finding algorithms

• Idea automatic search of parameter value
• which maximizes algorithm Score
• for a given event sample
• Abstract TunableVertexReconstructor class
• wrapper around the algorithm to tune
• TunableVertexReconstructorsetParameter(float
  value)
• TunableVertexReconstructorinitialRange()
• Concrete FineTuner1D class
• maximization algorithm
• divides initialRange() in N bins
• makes N clones of TunableVertexReconstructor
  with different parameter values, by
  setParameter(float value)
• computes Score for each
• zooms in or shifts range until parameter
  precision reached

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Conclusions

• We have developed an efficient class framework
  for the development of vertex fitting algorithms
• We have developed a friendly environment to
  evaluate and tune vertex finding algorithms
• A first version of the class framework for
  vertex finding algorithms is present
• improving while more algorithms get prototyped
• Now, time for implementations and results (next
  talk)

18
Backup slides
19
Problem definition
d0 lt 1 mm
Impact parameter resolutions

• d0 in tt (full), Wc (dashed), Wu,d,s,g (dotted)
• impact parameter of secondary tracks ltlt 1 mm

• ?(d0) f(pT,?)
• pT 1 GeV/c 0.1 ? 0.2 mm
• high pT 10 ? 20 ?m

• ?(z0) f(pT,?)
• pT 1 GeV/c 0.1 ? 1 mm
• high pT 20 ? 100 ?m

Primary and secondary tracks not well
separated Reconstruction in 3D global
optimization
20
Vertex fitting framework
UML diagrams
21
VertexFastSim framework
22
Vertex finding tuning framework
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Analysis (cont.)
Evaluation of vertex reconstruction performance

• Performance estimator classes (1 for each
  performance figure)
• Divided into
• vertex finding performance estimators
• vertex track assignment performance estimators
• Examples (see reference manual)
• VertexFindingEfficiencyEstimator
• VertexTrackAssignmentPurityEstimator
• You have to provide them with the Monte-Carlo
  truth, and the associators that you want them to
  use
• VertexAssociationToolsFactory provides 1
  VertexAssociator and 1 TrackAssociator that are
  consistent with each other
• type of associators configurable in .orcarc

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Analysis (cont.)

• These are all combined into a standard
  performance test VertexRecoPerformanceTest
• simulated vertices separated into primary and
  secondary vertices
• performance evaluated for each type separately
• only reconstructible simulated vertices
  considered
• 2 tracks reconstructed
• vertex association by tracks, successful if
  purity of RecVertex ? 50
• associated simulated vertices Efficiency
• unassociated reconstructed vertices Fake rate
• irrespective of primary or secondary
• track association by hits (default)
• specify by pulls if no hits
• used to evaluate purity and track assignment
  efficiency